Surface area of a pyramid = area of base + lateral surface area (total area of the triangles)
📘 Example ①
Find the surface area of a regular square pyramid with a square base whose side length is 6 cm and whose slant height is 5 cm.
Answer: Area of base = 6×6 = 36 cm².
One lateral triangle = (1/2)×6×5 = 15 cm². Four lateral triangles = 60 cm².
Surface area = 36 + 60 = 96 cm²
Find the surface area of a regular square pyramid with a square base whose side length is 6 cm and whose slant height is 5 cm.
Answer: Area of base = 6×6 = 36 cm².
One lateral triangle = (1/2)×6×5 = 15 cm². Four lateral triangles = 60 cm².
Surface area = 36 + 60 = 96 cm²
💡 Key Points
- Pyramid: 1 base + triangular lateral faces (the number of sides of the base)
- The “slant height” is the height of a lateral triangle (it is different from the height of the pyramid)
Practice Problem
- Find the surface area of a regular square pyramid with a square base whose side length is 4 cm and a slant height of 6 cm.
Answer and Explanation
- Answer: 64 cm². Base=16. Lateral surface area=(1/2)×4×6×4=48. Total=64.