Centroid of Two Shapes
Description
This applet illustrates computation of the centroid of a composite shape. The shape is a combination of a triangle and a rectangle. 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 areas and divide that by the sum of the individual areas as shown on the applet.
If the shapes overlap, the triangle is subtracted from the rectangle to make a new shape. When a shape is subtracted just treat the subtracted area as a negative area. It can often be easier to subtract an area rather than add an area. When the areas overlap the shape removed from the rectangle may not be a triangle but it is labeled as a triangle.
A table (or spreadsheet) as shown on the bottom is the best way to calculate the centroid of a shape made up of a combination of other shapes.
CentQ1 is the centroid of the rectangle, centT1 is the centroid of the triangle, and CentP1 is the centroid of the subtracted shape.
Activities
You can move the points, A,C, E, F and G to see how the composite centroid changes.
By placing the points as follows you can make an L shaped object. E @ (1,2), F@ (5,2) and G @ (1,-2). Try computing the centroid by using two rectangles to make up the same shape.