# Decomposing Bases for Area

Warmup

Activity #1

Explore 3-D Shapes.

In the applet below, you can find geometric tools under .

• Shade one base in the picture.

• Draw a cross section of the prism parallel to the base.

Activity #2

Explore Ways of Finding the Volume of 3-D Shapes.

A box of chocolates is a prism with a base in the shape of a heart and a height of 2 inches. Here in the applet below are the measurements of the base.

To calculate the volume of the box, three different students have each drawn line segments showing how they plan on finding the area of the heart-shaped base.

• Study the different plans and answer the questions below.

(1.) For each student’s plan, describe the shapes the student must find the area of and the operations they must use to calculate the total area.

(2.) Although all three methods could work, one of them requires measurements that are not provided. Which one is it?

Challenge #1

A house-shaped prism is created by attaching a triangular prism on top of a rectangular prism. Draw the base of this prism and label its dimensions.

Challenge #2

Find the volume of the crystal in the applet below.

Challenge #3

A rectangular prism with dimensions 5 inches by 13 inches by 10 inches was cut to leave a piece as shown in the image.

(1.) What is the volume of this piece above?

(2.) What is the volume of the other piece not pictured?

Quiz Time