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.

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.

## Square & Rectangular Pyramids

## Lateral Surface Area and Volume

Goals1. Use reasoning to calculate surface area.

2. Use the Pythagorean theorem as necessary to find missing dimensions.

BackgroundI 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 heightGiven: A square pyramid with base dimensions 6’ x 6’ and h=5’

This is Figure 6 from the Creating Solids page.

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 heightGiven: 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 heightGiven: A rectangular pyramid with base dimensions 6’ x 3’ and h=5’

This is Figure 8 from the Creating Solids page.

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

Step 1a - Find the slant height for the small triangular face (metal texture).

Step 1b - Compute the area of one 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