Question

In this activity, you will find the valine of a composite shape by decomposing it into simpler shapes such as cubes and rectangular prisms. the figure shows the dimension of a writing desk. Complete the steps below to find its volume.

Answer 1

Part A

The given shape can be split into three rectangular prisms.

Part B

There are two ways of breaking this shape into three rectangular prisms.

Part C

small rectangle 18 x 26 x 36.5

large rectangle 6.5 x 26 x 74.5

Part D

The length, width, and height of the small prism is 18 inches, 26 inches, and 36.5 inches so the volume is 17,082 cu in.

The length, width, and height of the small prism is 6.5 inches, 26 inches, and 74.5 inches so the volume is 12,590 cu in.

PART E

12,590 + 14,040 + 14,040 = 40,670.5 cu in.

The volume of the desk is the same for both options: 40,670.5 cubic inches. No matter how I divide the composite shape, the resulting volume is the same.