High School Geometry Test Questions on Pyramid Surface Area

📚 Quick Study Guide

• 📐 Basic Pyramid Definition: A pyramid is a polyhedron formed by connecting a polygonal base and a point, called the apex. Each base edge and apex form a triangle.
• ✨ Surface Area Components: The surface area of a pyramid is the sum of the area of its base and the area of all its lateral faces (the triangular faces).
• 📏 Lateral Area Formula: For a regular pyramid (a pyramid with a regular polygon as its base and congruent isosceles triangles as lateral faces), the lateral area (LA) can be found by: $LA = \frac{1}{2} * P * l$, where $P$ is the perimeter of the base, and $l$ is the slant height.
• ➕ Total Surface Area Formula: The total surface area (TSA) of a pyramid is: $TSA = LA + B$, where $LA$ is the lateral area and $B$ is the area of the base.
• 💡 Slant Height: The slant height is the height of one of the triangular faces, measured from the base to the apex along the face. It's NOT the same as the pyramid's height.
• 📝 Square Base Pyramid: If the base is a square with side $s$, then $B = s^2$ and $P = 4s$.
• ➗ Triangular Base Pyramid: If the base is an equilateral triangle with side $s$, then $B = \frac{\sqrt{3}}{4}s^2$ and $P = 3s$.

Practice Quiz

1. What is the formula for the lateral surface area of a regular pyramid, where P is the perimeter of the base and l is the slant height?
   1. A) $LA = P * l$
   2. B) $LA = \frac{1}{2} * P * l$
   3. C) $LA = B + \frac{1}{2} * P * l$
   4. D) $LA = B + P * l$
2. A square pyramid has a base side length of 6 cm and a slant height of 5 cm. What is its lateral surface area?
   1. A) 30 cm²
   2. B) 60 cm²
   3. C) 96 cm²
   4. D) 120 cm²
3. What is the total surface area of a square pyramid with a base side of 4 cm and a slant height of 6 cm?
   1. A) 48 cm²
   2. B) 64 cm²
   3. C) 80 cm²
   4. D) 96 cm²
4. An equilateral triangular pyramid has a base side of 8 cm and a slant height of 10 cm. What is the lateral surface area?
   1. A) 40 cm²
   2. B) 80 cm²
   3. C) 120 cm²
   4. D) 240 cm²
5. If the lateral surface area of a square pyramid is 80 cm² and the perimeter of the base is 20 cm, what is the slant height?
   1. A) 4 cm
   2. B) 6 cm
   3. C) 8 cm
   4. D) 10 cm
6. A regular hexagonal pyramid has a base side length of 2 inches and a slant height of 5 inches. What is its lateral area?
   1. A) 15 inches²
   2. B) 30 inches²
   3. C) 60 inches²
   4. D) 120 inches²
7. What is the total surface area of a triangular pyramid where the base is an equilateral triangle with side 4 cm and the slant height is 7 cm? (Round to 2 decimal places.)
   1. A) 46.93 cm²
   2. B) 48.73 cm²
   3. C) 50.73 cm²
   4. D) 52.93 cm²