1. Lateral and Total Surface Area
10.3
Lateral and Total Surface Area
How do you find the lateral and total surface area of rectangular and triangular prisms or pyramids?

2. ADDITIONAL EXAMPLE 1
A net of a rectangular prism is shown. Use the net to find the lateral area and the total surface area of the prism. Each square represents one square foot. The blue regions are the bases, and the green regions are the lateral faces.
32 ft2; 62 ft2

3. ADDITIONAL EXAMPLE 2
Use the net of the rectangular pyramid to find the lateral area and the total surface area of the pyramid.
168 m2; 228 m2

4. ADDITIONAL EXAMPLE 3
Students built a model of a square pyramid for a social studies project. The sides of the square base are 18 inches long. The height of each triangular face is 12 inches. They want to cover the pyramid in plastic wrap that costs $0.16 per square inch. How much more money will it cost to cover the total surface of the pyramid than to cover the lateral surface?
$51.84

5. 10.3 LESSON QUIZ
7.9.D 1.
Find the lateral area and the total surface area of the prism.
816 m2; 1,086 m2

6. 2.
Find the lateral area and the total surface area of the pyramid.
912 mm2; 1,488 mm2

7. 3.
Compare the cost of covering the lateral area and the total surface area of the prism below with foil that costs $0.23 per square inch.
lateral area: $158.70; total surface area:
$172.50; Covering the total surface costs
$13.80 more.

8. What is the surface area of the milk carton. Describe how you found it
What is the surface area of the milk carton? Describe how you found it. See if you can find another way to find it.

9. The bottom is a rectangular prism with one base
The bottom is a rectangular prism with one base. The surface area is 4(8)(3) + 3(3) = 105 in2. The top is a triangular prism without one lateral surface. The surface area is 2(3)(2.5) + 2(1.5)(2) = 21, so the surface area is = 126 in2.
A second way to find the surface area would be to find the surface areas of the enclosed top and bottom figures, and then subtract the middle surface for each figure.

10. How do you find the lateral and total surface area of rectangular and triangular prisms or pyramids?
Sample answer:
Find the area of each face. Then add the areas to find the lateral area. To find the total area, add the area of each base to the lateral area.