The entire area of such a plane figure may be assumed to be concentrated at a point, which is known as the centroid of the area. The point in which the three medians of the triangle intersect is known as the centroid of a triangle. The first theorem of Pappus states that the surface area S of a surface of revolution generated by the revolution of a curve about an external axis is equal to the product of the arc length s of the generating curve and the distance d_1 traveled by the curve's geometric centroid x^_, S=sd_1=2pisx^_ (Kern and Bland 1948, pp. Online Semicircle Calculator | Free Handy Calculator Tool ... ), prove that arc CXA + arc DZB = arc AYD + arc BWC = semicircle. W x ⦠The following points show the properties of the centroid of a triangle which are very helpful to distinguish the centroid from all the other points of concurrencies.. Centroid of semicircle is at a distance of 4R/3Ï from the base of semicircle. Explanation of the Centroid Theorem. Strength of Materials: The Centroid of a Semicircle. A x ¯ = â« a b x c d A. To calculate Y C we need to calculate M X = , where dA represents as strip from x 1 to x 2 (see figure 6) From the equation of the circle we get . Centroid Calculator is a free online tool that displays the centroid of a triangle for the given coordinate points. This group is given by the euler number. Fig.7.4 Centroid of a semicircle. Solved Consider the shaded composite shape consisting of a ... ⢠The centroid of a 2D surface is a point that corresponds to the center of gravity of a very thin homogeneous plate of the same area and shape. Semicircle Calculator: It is a one stop destination to solve any semicircle problem.Here, you will get the calculators that computes semi circle area, radius, diameter, and perimeter. Find the centroid of the semicircle shown on your screen now (be sure to notice where the axes are! The centroid of a body does not change if we change its position. Centroid L x ¯ = â« a b x c d L. L y ¯ = â« a b y c d L. Center of gravity of bodies. Get all of Hollywood.com's best Movies lists, news, and more. You shall note that it is not possible to divide a semicircle in a few appropriate standard-areas, for each of which magnitude with location of its centroid is known. The Volume of a Semicircle calculator computes the volume of a semicircular shape based on the radius (r) and the height (h).. When the vertices are known, the centroid calculator will easily find centroid of any 2 ⦠b) Calculate the area of the shape. Use this online geometric Centroid of a Semicircle Calculator to calculate the semicircle centroid with radius r. The following table ⦠Centroid of a semicircle wire. â¢Calculate the first moments of each area with respect to the axes. It is the point that matches to the center of gravity of a particular shape. The centroid of a trapezoid formula in mathematics is given as â. Feel free to also answer the questions after. ⦠If the axis passer through the centroid, the moments of areas on one side of the axis will be equal to the moments of areas on the other side of the axis. Download Object. Using the structural engineering calculator located at the top of the page (simply click on the the "show/hide calculator" button) the following properties can be calculated: Calculate the Area of a Hollow Circle or Annulus; Calculate the Perimeter of a Hollow Circle or Annulus; Calculate the Centroid of a Hollow Circle or Annulus Thus the centroid of the semicircle shown is at . If the object has a uniform density, then the center of mass will be located at the centroid. [NCERT Exemplar Problem] Answer. Finding Centroid of a Semicircle. The centroid of a semicircle is different from semicircular arc since it has all of its mass. We can further use the parallel axis theorem to prove the expression where the triangle centroid is located or found at a distance equal to h/3 from the base.. 3. 6.0 inches from the bottom. The equation for the centroid curve is: y = 693. Use this online geometric centroid of a semicircle calculator to calculate the semicircle centroid with radius r. Download. If you want to calculate the centroid of a right triangle or centroid of a trapezoid using this calculator, follow the steps below: Enter coordinates for x1 and y1 Enter coordinates for x2 and y2 Enter coordinates for x3 and y3 Press the Calculate button to get the coordinates of the centroid. ... Area of Semicircle Calculator. Centroid, Area, Moments of Inertia, Polar Moments of Inertia, & Radius of Gyration of a Semi-Circular Cross-Section Home Calculators Forum Magazines Search Members Membership Login and therefore . Going through it as a semi-circle: ȳ=2R/pi=2*(1.366)/pi=.8696. We can calculate the centroid by taking the average of the x-coordinates and the y-coordinates of the vertices of the triangle. It is the point through which all the mass of a triangular plate seems to act. Find the centroid of each subarea in the x,y coordinate system. Circular Segment. As with all risk calculators, calculated risk numbers are +/- 5% at best. The centroid is the term for 2-dimensional shapes. I Beam Centroid Calculator. respectively on the circumference of the circular park with centre O and radius 10 m. Since the centre of circle coincides with the centroid of the equilateral âABC. The compressive area would be a semicircle, with area The centroid is the centre point of the object. Divide the composite area into simpler areas for which 3. The moment of inertia is a geometrical property of a beam and depends on a reference axis. Semicircle Perimeter Calculator: People who are searching for a best tool that calculates the perimeter of a semicircle can stay on this page.Here, we are giving the detailed step by step procedure that is helpful for you to solve the perimeter without any difficulty. Hence, centroid from reference Y-axis. Lastly, compute the centroid given the formula: C x = âC ix A ix / âA ix C y = âC iy A iy / âA iy Step-By-Step Procedure in Solving for the Centroid of Compound Shapes in problem 46. Example: Find the position of the centroid of ⦠Y centroid of a ⦠The angle at the circumference in a semicircle is a right angle. Centroids Determined by Integration. How to Calculate Centroid (Centroid Equation): Consider the I-beam section shown below. Given two chords AB and CD of a circle intersect at right angle. Centroid is defined as the centre mass of a geometric object which has uniform density. A centroid is the point of intersection of the medians of the triangle. Sure, the equation i used is 4*R/3pi, in my case it was (4*4in)/ (3*Pi) which gives me 1.69765in, which is the distance from the center towards x-direction. Problem 722 Locate the centroid of the shaded area in Fig. Centroids and Center of Mass By Integration Example 1 Given: It is desired to determine the area and centroids of the shaded shape. x = 4 r / (3 Ï) (4a) y = r (4b) Area. INSTRUCTIONS: Choose units and enter the following: (h) Height of the semicircle shape(r) Radius of the semicircle shapeSemicircle Volume (V): The calculator returns the volume in cubic meters.However, this can be automatically ⦠Centroid & Center of Mass of a Semicircle The centroid is the point at the exact center of an object. Half the circle is termed as the semicircle. Let's implement the above formulas in a Java program and find the area of the circle. The hexagon is the highest regular polygon which allows a regular tesselation (tiling). With this semicircle area calculator, you can quickly find the area of half of a circle.What is more, the tool also doubles as a semicircle perimeter calculator, so inputting radius or diameter will help you find the basic features of the shape in the blink of an eye.In the article below, we provide the semicircle definition and explain how to find the perimeter and area of a ⦠Thus, M.O.I will be half the moment of inertia of that of a full circle. 1 ² = 1. Centroid of a semicircle using integration. The centroid of a rectangle is in the center of the rectangle, , and the centroid of triangle can be found as the average of its corner points, .To calculate the centroid of a combined shape, sum the individual centroids times the individual ⦠Centroid of area. This indicates that the centroid lies on y-axis. Substituting y = R sin θ , we get . Centroid of a circle is very easy to determine. Centroid of circle lies at the center of a circle that is also called as the radius of circle from edges of a circle. As shown below. Find the center of gravity (centroid) of circular wheel whose diameter is 20cm. Centroid of rectangular wall. Use this online geometric Centroid of a Semicircle Calculator to calculate the semicircle centroid with radius r. Inputs the 3 vertices of the triangle and outputs the centroid and graph of the triangle. W x ⦠About Centroid of a Triangle Calculator: This centroid of triangle calculator enables you to find the coordinates on the centroid of a triangle ABC, the centroid of any N-Points, and N-sided Polygon. The above formulas are great if the origin and the centroid coincide, but in reality that wonât always be the case. ... For the 2nd question - ⦠= 28 / 9.4247 C.G. The centroid of a rectangle is in its center. ⢠If the area (or section or body) has one line of symmetry, the centroid will lie somewhere along the line of symmetry. 1 While Loops. From symmetry, we can see that the centroid lies along the y-axis, which acts like a mirror to the quarter circles either side. Table.1. Get the free "Centroid - y" widget for your website, blog, Wordpress, Blogger, or iGoogle. Use this online geometric centroid of a semicircle calculator to calculate the semicircle centroid with radius r. Download . We just need to determine how far up this point is. Determine The Moments Of Inertia About X And Y A For Beam That Has Following Cross Sectional Area Coordinates Centroid Surface Hemisphere. Calculate the first moments of each area with respect to the axes. 110-111). the respective distance of the centroid of the tensile area. It is always considered with respect to a reference axis such as x - x or y-y ( Fig. "1" and "7" are distinguished by the skeleton length. A y ¯ = â« a b y c d A. Centroid of lines. Find more Mathematics widgets in Wolfram|Alpha. Solution. Semicircle: how to calculate perimeter, area, centroid, exercises The emicircle It i a flat figure delimited by a diameter of the circumference and one of the two flat circular arc determined by aid diameter.In thi way, a emicircle i bordered by a emicircumference, Content: Elements and measures of a semicircle Find out the centroid of an area of a semicircle: Find out the centroid of an area of a semicircle illustrated in Figure. This website uses cookies to ensure you get the best experience on our website. Examples on Calculating Centroid. Hexagon Calculator. = 4 (7) / 3Ï C.G. of area and the perpendicular distance of its centroid from the given line. It also refers to the center of mass of a geometric object. I x = I y = â
Ïr 4 = â
(A o) R 2 = â
(Ïr 2) R 2 Now to determine the semicircleâs moment of inertia we will take the sum of both the x and y-axis. Below I have shown the calculation of distance from initial centroids D2 and D4 from data point D1. To start using the free centroid calculator to calculate moment of inertia, simply choose the cross section you want to evaluate from the drop down list, then enter in the dimensions and click Calculate. The centroid of an area is the point where the whole area is considered to be concentrated. = 2.97 Therefore, the centroid or centre of gravity of the semicircle is 2.97. Let The general expression of centroid of a body is given by: Circle Segment - Geometric Propertie . 494 0 The correct answer is 4r/3pi, if what you are after is the average y-coordinate. Centroid calculator is an online tool that can be used to calculate the centroid of a triangle. The Centroid of Triangle is also known as 'center of gravity ', 'center of mass', or 'barycenter'. Image will be uploaded soon Centroid from reference X-axis; 61), the area is (1-. Centroid â The plane areas such as triangle, quadrilateral, circle, etc have only areas but no mass. a) Calculate the distance (positive value) in meters from the centroid of the semicircle to the x-axis. If the three vertices of the triangle are A (x 1, y 1), B (x 2, y 2), C (x 3, y 3), then the centroid of a triangle can be calculated by taking the average of X and Y coordinate points of all three vertices. Therefore, the centroid of a triangle can be written as: Centroid of a triangle = ((x 1 +x 2 +x 3)/3, (y 1 +y 2 +y 3)/3) Centroid of a semicircle ring. These theorems are very useful when calculating the centroid of a given area. Looking at your attachment this is an engineering question about the CofG ⦠Area of pipe: A1-A2=1.43193 in 2. Just enter the expression to find the ⦠2 - 1, 10, 19, 28 1. Transcript ENGINEERING MECHANICS STATICS THIRTEENTH EDITION This page intentionally left blank ENGINEERING MECHANICS STATICS THIRTEENTH EDITION R. C. HIBBELER Upper Saddle River Boston Columbus San Francisco New York Indianapolis London Toronto Sydney Singapore Tokyo Montreal Dubai Madrid Hong Kong Mexico City Munich Paris Amsterdam ⦠1. Hence, centroid from reference Y-axis. All of the above results assume that the body has constant density. The Volume of a Semicircle calculator computes the volume of a semicircular shape based on the radius (r) and the height (h).. For very simple shapes like rectangles or circles, it's easy to find the centroid because it's just in the middle of the shape. Where: r = Radius of the Semicircle This is the point to which a force may be applied to cause a linear acceleration without an angular acceleration. Perimeter of a Semicircle radius 8 m is 41.12 m . Question 1: Find the centroid of the triangle whose vertices are A(2, 6), B(4, 9), and C(6,15). This is because the outputs of the theorems (area, volumes of standard geometries) are already known to us. Use this online geometric Centroid of a Semicircle Calculator to calculate the semicircle centroid with radius r. Properties of the Centroid. Nickzom Calculator â The Calculator Encyclopedia is capable of calculating the centre of gravity of a semicircle at a distance from its base measured along the vertical radius. Centroid can be located in the shape or figure using various. Centroid of a Semicircle Calculator. To say that a circle has a circumference of 2\pi radians or just 2\pi, are the same thing, because the unit âradianâ is the same as saying âoneâ. Sure, the equation i used is 4*R/3pi, in my case it was (4*4in)/ (3*Pi) which gives me 1.69765in, which is the distance from the center towards x-direction. Use this online geometric Centroid of a Semicircle Calculator to calculate the semicircle centroid with radius r. Half the circle is termed as the semicircle. We want to revolve this same circle about this line. Square. Solution: Centroid of rectangular section lies where two diagonals intersect each other. Revolving the quarter-circle of radius $ \ ⦠Centroid for the defined shape is also calculated. Where the centroid coordinates About The Author Centroid of a semicircle arc of radius ârâ is. L x ¯ = â« a b x c d L. L y ¯ = â« a b y c d L. Center of gravity of bodies. Centroid is defined as the centre mass of a geometric object which has uniform density. Perimeter of an Equilateral Triangle Calculator: The Equilateral triangle perimeter calculator is a free online tool that supports students to calculate the perimeter of an equilateral triangle easily. Perimeter of an Equilateral Triangle Calculator. I think you are confusing a semicircular area with a semicircular arc. Alternatively, try our free Centroid Calculator: Free Centroid Calculator. Distance Calculation. The centroid of Semicircle \( (0, \frac{4r}{3\pi}) \) Circumference of Semicircle Formulas \( P = \pi r \) Summary of Semicircle Formula. â Investigate, justify, and apply theorems about mean proportionality: * the altitude to the hypotenuse of a right triangle is the mean proportional between the two segments along the hypotenuse * the altitude to the hypotenuse of a right triangle divides the hypotenuse so that either leg of the right triangle is the mean ⦠â¢Compute the coordinates of the area centroid by dividing the first moments by the total area. The steps for the calculation of the centroid coordinates, x c and y c , of a composite area, are summarized to the following: Select a coordinate system, (x,y), to measure the centroid location with. Then click Calculate. For each two-dimensional shape below, the area and the centroid coordinates ( x ¯ , y ¯ ) {\displaystyle ({\bar {x}},{\bar {y}})} are given: 1. Area of ⦠Math is Fun Curriculum for High School Geometry. Centroid of Semi-circle Formula: Example Find the centroid of semi-circle whose radius is 10cm and of 20cm diameter. Switch branches ×. A y ¯ = â« a b y c d A. Centroid of lines. The centroid of a semicircle is located 4r/3Ï above the base (diameter) of the semi-circle of radius r. A. The centroid is an important property of a triangle. When calculating the first moment, shouldn't you use the distance from the center of the ring to the centroid instead of the centroid? Find the centroid of rectangular wall whose height is 12 ft. and base length of wall is 24 ft. Consider a vertical strip of infinitesimally small thickness âdxâ at any âxâ having height of âyâ. Critical Number Calculator. centroid of the volume under the distributed ... rectangle, and semicircle with a circular cutout. Enter one value and choose the number of decimal places. Decompose the total area to a number of simpler subareas. Polyhedron Centroid Calculation Algorithm. Now this gives us: Ix = Iy = â
Ïr 4 = â
(Ao) R 2 = â
Ïr 2) R 2. For none constant density see the general integral forms of Mass, Mass Moment of Inertia, and Mass Radius of Gyration. Answer (1 of 3): Angles expressed in radians are actually dimensionless. Centroid of area. Calculations at a semicircle. c) ⦠Use this online geometric Centroid of a Semicircle Calculator to calculate the semicircle centroid with radius r. Properties of the Centroid. NOTE: ; is the mass of the entire body. Read this entire page, to get the complete knowledge on this topic. Centroid Definition. Examples. Another (related $ ^* $) method for locating the centroid of a region with constant density is to apply Pappus' (Second) Centroid Theorem, which states that the volume of a solid of revolution is equal to the area of the region revolved about the rotation axis times the circumference of the circle swept out by the centroid.. This page references the formulas for finding the centroid of several common 2D shapes. Find the solved examples below, to find the centroid of triangles with the given values of vertices. In the figures, the centroid is marked as point C. Its position can be determined through the two coordinates x c and y c , in respect to the displayed, in every case, Cartesian system of axes x,y. Thank you very much in advance! To see why, look at the definition of ⦠Use this online geometric Centroid of a Semicircle Calculator to calculate the semicircle centroid with radius r. The centroid divides each median into parts in the ratio 2:1, with the centroid being twice as close to the midpoint of a side as it is to the opposite vertex. It motivates as well as nurture the students to make him a responsible citizen. When another centroid is added the distortion decreases to 130. Centroid calculator will also calculate the centroid from the defined axis, if centroid is to be calculated from origin x=0 and y=0 should be set in the first step. The centroid method can benefit any type of business that transports materials or goods and wants to improve profits by making the best transportation decisions. For example, car manufacturing companies commonly utilize the centroid method. This industry involves the transport of very large volumes of product over long distances. C. 6.4 inches from the bottom. 40. Centroid of semicircle is at a distance of 4r 3Ï from the base of semicircle. r = radius of the semicircle = 7 C.G. Bye equals C. And we know that the central for this semicircle lies at this point at X equals zero. Centroid of a semicircle arc. Find more Mathematics widgets in Wolfram|Alpha. All of the above results assume that the body has constant density. This applet illustrates computation of the centroid of a composite shape. Christiansen (Twitter). Centroid of a semicircle Centroid of a semicircle calculator. M.O.I relative to the origin, J o = I x + I y = â
Ïr 4 + â
Ïr 4 = ¼ Ïr 4 Derivation We will basically follow the polar coordinate method. Centre of Mass (Centroid) for a Thin Plate. This gives . Academia.edu is a platform for academics to share research papers. Visual Mathematics Dictionary www.education2000.com. 2 ft 3 ft 4 ft â 0 0 0 0 The moment of inertia of the semicircle about the x-axis is Calculations at a semicircle. So,the centroid of triangle can be found by finding the average of the x-coordinate's value and the average of the y ⦠The centroid of a trapezoid formula in mathematics is given as â. Heights, bisecting lines and median lines coincide, these intersect at the centroid, which is also circumcircle and incircle center. Solution: Centroid of rectangular section lies where two diagonals intersect each other. Formula(s) Substitute / Solve Final Answer 2. 2) More Complex Shapes:. Calculate the x-coordinate, in feet, of the centroid of the shaded composite shape. 0. and semicircle with a circular cutout. The centroid is also known as the geometric center of the object. eps) Portable Document Format (. Furthermore, the regular pentagon is ⦠You can use the view menu button to add fuctionality to the standard calculator. "3" is the only one, in the other group, with 3 endpoints. 1) Rectangle: The centroid is (obviously) going to be exactly in the centre of the plate, at (2, 1). 2. P-722 created by cutting a semicircle of diameter r from a quarter circle of radius r. The centroid of a triangle is the point of intersection of all the three medians of a triangle. Calculating the centroid involves only the geometrical shape of the area. All shapes have centroids. Centroid of semicircle is at a distance of 4R3Ï from the base of semicircle. The y -coordinate is given by: 2. We want to revolve this same circle about the line y equals a. math dictionary to view the specific definition for each math term. Here, the semi-circle rotating about an axis is symmetric, and therefore, we consider these values equal. Let us discuss the definition of centroid, formula, properties and centroid for different geometric shapes in detail. 2 ft 3 ft 4 ft â 0 0 0 0 ; Question: Consider the shaded composite shape consisting of a rectangle, triangle and semi-circle. Download Object. Calculations at a regular hexagon, a polygon with 6 vertices. Now to find the moment of inertia of the semicircle we will take the sum of both the x and y-axis. Privacy Policy OK 𩺠#columbiamed #whitecoatceremonyâ NOTE: ; is the mass of the entire body. The x-centroid would be located at 0 and the y-centroid would be located at 4 3 r Ï 7 Centroids by Composite Areas Monday, November 12, 2012 Centroid by Composite Bodies ! A Centroid is the point where the triangleâs medians intersect. To this point, the regular pentagon is rotationally symmetric at a rotation of 72° or multiples of this. Divide the composite area into simpler areas for which 3. Centroids of common shapes of areas. We divide the complex shape into rectangles and find `bar(x)` (the x-coordinate of the centroid) and `bar(y)` (the y-coordinate of the centroid) by taking moments about the y-and x-coordinates ⦠To compute the centroid or centre of gravity of a semicircle, you need one essential parameter and this parameter is the radius of the semicircle. If two chords AB and CD of a circle AYDZBWCX intersect at right angles (see fig. Problem 722 Locate the centroid of the shaded area in Fig. Example 3.2 Locate the centroids if the trapegezium as shown in figure 3.09 Fig 3.09 Solution Important â Note 1. find the endpoint 12. com Images. 1,812 Likes, 63 Comments - Mitch Herbert (@mitchmherbert) on Instagram: âExcited to start this journey! A centroid is the central point of a figure and is also called the geometric center. If the the coordinate points of the right angled triangle are (3,1) , (2,6) and (3,4), the centroid can be calculated as = [ ( 3 + 2 + 3 ) / 3 , ( 1 + 6 + 4 ) / 3 ] = [ ( 8 / 3 ) , ( 11 / 3 ) ] = [ 2.6667 , 3.6667 ] B. Calculate centroid of all points within the cluster; Repeat iteratively till convergence. Surface Area and Volume of a Torus. The shape is a combination of a triangle and a rectangle. Find the area of the shaded region calculator. m Submit part 1.5 marks Unanswered b) Calculate the distance (positive value) in meters from the; Question: na bab а b In the figure above, the curved area that is cut out from the rectangle is a semicircle. is the density of the body. If we wanted the centroid with respect to another axis, say along the top of the semicircle and along the left edge, the values in the table couldnât be used exactly x y C 5 circles in circles codehs answers. Distance. If the radius of the circle is \(r\) and the distance from the center of circle to the axis of revolution is \(R,\) then the surface area of the torus is P-722 created by cutting a semicircle of diameter r from a quarter circle of radius r. For none constant density see the general integral forms of Mass, Mass Moment of Inertia, and Mass Radius of Gyration. A portion of a disk whose upper boundary is a (circular) arc and whose lower boundary is a chord making a central angle radians (), illustrated above as the shaded region.The entire wedge-shaped area is known as a circular sector.. Circular segments are implemented in the Wolfram Language as DiskSegment[x, y, r, q1, q2].Elliptical segments are ⦠The only unknown quantity is the location of centroid. Triangle Centroid Calculator Added Feb 6, 2014 by Sravan75 in Mathematics Inputs the 3 vertices of the triangle and outputs the centroid and graph of the triangle. Examples. The given below is the online critical number calculator for you to calculate the same. Find: For the shaded shape provided, a) Estimate the area and the x and y centroids. For the left semicircle the centroid is at x=-4r/3pi, but I'm not sure how to tackle the right part to ultimately find the total centroid. Indeed, if c is an endpoint of the domain of f ( x ), then f ( x ) is said to have an endpoint ⦠In this animated and interactive object, learners calculate the area and centroid of a semicircle. Centroid of semicircle is at a distance of 4R/3Ï from the base of semicircle. Enter one value and choose the number of decimal places. Centroids Determined by Integration. Half the circle is termed as the semicircle. Find the centroid of the semicircle shown on screen now: Because the semicircle is centered about the y -axis, the x -coordinate of the centroid is zero. Find the location of the centroid of the composite area consisting of a 10-inch square surmounted by a semi-circle. This can be calculated fairly easily by doing this: (1/A) S [y*2sqrt (1-y^2)dy] from 0 to 1. â¢Find the total area and first moments of the triangle, rectangle, and semicircle. Find resources for Government, Residents, Business and Visitors on Hawaii.gov. Much like the centroid calculations we did with 2D shapes, we are looking to find the shape's average coordinate in each dimension. C = Distance to Centroid, in or mm I = Second moment of area, in4or mm4 Ji= Polar Moment of Inertia, in4or mm4 K = Radius of Gyration, in or mm P = Perimeter of shape, in or mm Z = Elastic Section Modulus, in3or mm3 Online Half Circle Property Calculator The centroid of a rectangle is in its center. Get the free "Centroid - y" widget for your website, blog, Wordpress, Blogger, or iGoogle. Use the 7 + 5 Chords to compose your own songs. Centroids - Reference Table. Find the centroid of rectangular wall whose height is 12 ft. and base length of wall is 24 ft. Centroid calculator is an online tool that can be used to calculate the centroid of a triangle. Thus, the length of each string is 10â3 m. (ii) In studentsâ life, discipline is necessary. A x ¯ = â« a b x c d A. To calculate the centroid of the semicircle shown in figure 2, we need to calculate its area A as follows: The equation of the circle is x2 + y2 = r2 where r is its radius.