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.

Explanation:

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

Hence, the surface area of the square pyramid with a side of 4 cm and a height of 5 cm is 59.08 cm².