Lesson 13: Decomposing Bases for Area

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, $B$ , and multiply that by the height, $h$ .

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

$\displaystyle V = Bh$

Visual / Anchor Chart

Standards

Addressing

7.G.3

Describe the two-dimensional shapes that result from slicing three-dimensional solids parallel or perpendicular to the base.

7.G.6

Solve real-world and mathematical problems involving area of two-dimensional objects composed of triangles and trapezoids. Solve surface area problems involving right prisms and right pyramids composed of triangles and trapezoids. Find the volume of right triangular prisms, and solve volume problems involving three-dimensional objects composed of right rectangular prisms.