Question

find the total surface area of this square-based pyramid.

Explanation:

Step1: Calculate base area

The base is a square with side \( 5 \) in. Area of square: \( 5 \times 5 = 25 \) \( \text{in}^2 \).

Step2: Calculate lateral surface area

There are 4 triangular faces. Each triangle has base \( 5 \) in and slant height \( 10 \) in. Area of one triangle: \( \frac{1}{2} \times 5 \times 10 = 25 \) \( \text{in}^2 \). Total lateral area: \( 4 \times 25 = 100 \) \( \text{in}^2 \).

Step3: Calculate total surface area

Add base and lateral areas: \( 25 + 100 = 125 \) \( \text{in}^2 \).

Answer:

\( 125 \)