# Lateral Surface Area and Volume

Goals
1. Use reasoning to calculate surface area.
2. Use the Pythagorean theorem as necessary to find missing dimensions.

Background
I have included the videos from Creating Solids page in order to review these specific pyramids. I strongly suggest working through the nets exercises before completing these examples. My students benefit from having a paper model to fold and unfold.

Example 1: Find the Lateral Surface area of a Square Pyramid with a given height
Given: A square pyramid with base dimensions 6’ x 6’ and h=5’
This is Figure 6 from the Creating Solids page.

 Figure 6 - Cutaway

Step 1 - Find the slant height
Step 2 - Find the area of one triangular face
Step 3 - Find the lateral surface area

Extension - Find the volume of this square pyramid.

Example 2: Find the Lateral Surface area of a square pyramid with a given slant height
Given: A square pyramid with base dimensions 6’ x 6’ and slant height = 5’
This is Figure 7 from the Creating Solids page.

Step 1 - Find the slant height (given)
Step 2 - Find the area of one triangular face
Step 3 - Find the lateral surface area

Extension - Find the volume of this rectangular pyramid.

Example 3: Find the Lateral Surface area of a rectangular pyramid with a given height
Given: A rectangular pyramid with base dimensions 6’ x 3’ and h=5’
This is Figure 8 from the Creating Solids page.

 Figure 8 - Cutaway

Use SketchUp to show the interior right triangles. Be careful!

 Figure 8 - Small Face

Step 1a - Find the slant height for the small triangular face (metal texture).
Step 1b - Compute the area of one face.

 Figure 8 - Large Face

Step 2a - Find the slant height for the large triangular face (wavy texture).
Step 2b - Compute the area of one face.
Step 3 - Find the lateral surface area

Extension - Find the volume of this rectangular pyramid.

SOLUTIONS PAGE

Updated August 2017