Decomposing Bases for Area

Student Summary

To find the area of any polygon, you can decompose it into rectangles and triangles. There are always many ways to decompose a polygon.

Four images of the same irregular polygon. In two images, the polygon is cut into different triangles and rectangles. In the fourth image, a triangle is added to make the polygon a rectangle.

Sometimes it is easier to enclose a polygon in a rectangle and subtract the area of the extra pieces.

To find the volume of a prism with a polygon for a base, you find the area of the base, BB, and multiply that by the height, hh.

A prism. The base of the prism is the irregular polygon from the previous images, area B, and the prism has height h.

V=Bh\displaystyle V = Bh

Visual / Anchor Chart

Standards

Addressing
7.G.3

7.G.A.3

7.G.6

7.G.B.6

7.G.6

7.G.B.6