Question

the square pyramid below has a height of 12 centimeters and a slant height of 20 centimeters. the square base of the pyramid has side lengths of 32 centimeters. what is the lateral area of the pyramid? $\bigcirc$ $384\\ \text{cm}^2$ $\bigcirc$ $640\\ \text{cm}^2$ $\bigcirc$ $768\\ \text{cm}^2$ $\bigcirc$ $1280\\ \text{cm}^2$

Explanation:

Step1: Find area of one triangular face

The area of a triangle is $\frac{1}{2} \times \text{base} \times \text{slant height}$. Here, base = 32 cm, slant height = 20 cm.
$\text{Area of 1 triangle} = \frac{1}{2} \times 32 \times 20 = 320 \text{ cm}^2$

Step2: Calculate total lateral area

A square pyramid has 4 identical triangular lateral faces.
$\text{Total lateral area} = 4 \times 320 = 640 \text{ cm}^2$

Answer:

640 cm²