# 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 cm^{2}.

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 = √(a^{2}/4 + h^{2}) using the Pythagoras theorem.

Hence, the total surface area of square pyramid A = a^{2} + 1/2 × (4a) × (√(a^{2}/4 + h^{2}))

Therefore, A = 4^{2} + 1/2 × [4 × 4)] × [√(4^{2}/4 + 5^{2})]

= 16 + 8 × √29 ≈ 59.08 cm^{2}

### Hence, the surface area of the square pyramid with a side of 4 cm and a height of 5 cm is 59.08 cm^{2}.

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