Use a formula to find the surface area of the square pyramid with a side of 4 cm and a height of 5 cm.
Pyramids are interesting solid shapes that have numerous practical applications in engineering and architecture. Square pyramids have a square-shaped base.
Answer: The surface area of the square pyramid with a side of 4 cm and a height of 5 cm is 59.08 cm2.
Let's understand the solution in detail.
In the given figure, we have base length = a = 4 cm, and height = h = 5 cm.
The total surface area of square pyramid = Base Area + 1/2 × (perimeter of the base) × (slant height)
Here, the slant height = √(a2/4 + h2) using the Pythagoras theorem.
Hence, the total surface area of square pyramid A = a2 + 1/2 × (4a) × (√(a2/4 + h2))
Therefore, A = 42 + 1/2 × [4 × 4)] × [√(42/4 + 52)]
= 16 + 8 × √29 ≈ 59.08 cm2