Lesson 3: Surface Areas of Pyramids — Practice Questions

1. 1. A triangular pyramid has a base with an area of $20 \text{ in}^2$. Each of its three lateral faces has an area of $18 \text{ in}^2$. What is the total surface area of the pyramid? ___ $\text{in}^2$

2. 2. Which statement best describes how to find the surface area of a triangular pyramid?

   • A. Multiply the area of the base by four.
   • B. Add the area of the base to the area of one lateral face.
   • C. Add the areas of the three lateral faces.
   • D. Add the area of the base to the areas of the three lateral faces.

3. 3. A regular triangular pyramid has a base area of $27.7 \text{ m}^2$ and a slant height of $10$ m. If the side length of the triangular base is $8$ m, what is the pyramid's total surface area? ___ $\text{m}^2$

4. 4. The total surface area of a regular triangular pyramid is $100 \text{ cm}^2$. If the area of its base is $25 \text{ cm}^2$, what is the area of a single lateral face? ___ $\text{cm}^2$

5. 5. A regular triangular pyramid has a base area of $43.3 \text{ ft}^2$. The side length of its base is $10$ ft and its slant height is $12$ ft. What is its total surface area?

   • A. $103.3 \text{ ft}^2$
   • B. $180.0 \text{ ft}^2$
   • C. $223.3 \text{ ft}^2$
   • D. $173.2 \text{ ft}^2$

6. 6. A regular square pyramid has a base side length of 4 inches and a slant height of 7 inches. What is its total surface area in square inches? ___

7. 7. The surface area of a square pyramid is calculated by adding the area of its square base to what other quantity?

   • A. The area of one triangular face
   • B. The area of two triangular faces
   • C. The area of four triangular faces
   • D. The perimeter of the base

8. 8. A square pyramid has a base with an area of 49 square feet and a slant height of 9 feet. Calculate its total surface area in square feet. ___

9. 9. A square pyramid has a base side length of 10 meters and a slant height of 12 meters. What is the area of its lateral faces?

   • A. $100 m^2$
   • B. $120 m^2$
   • C. $240 m^2$
   • D. $340 m^2$

10. 10. A square pyramid has a total surface area of 200 square cm and a base side length of 10 cm. What is its slant height in cm? ___