Question

a square pyramid is shown below.

image of a square pyramid with base edge 4 cm, slant height 6 cm

what is the surface area of the pyramid?

□ square centimeters

Explanation:

Step1: Find base area

The base is a square with side \( 4 \, \text{cm} \). Area of base: \( 4 \times 4 = 16 \, \text{cm}^2 \).

Step2: Find lateral face area

Each lateral face is a triangle with base \( 4 \, \text{cm} \) and height \( 6 \, \text{cm} \). Area of one triangle: \( \frac{1}{2} \times 4 \times 6 = 12 \, \text{cm}^2 \).

Step3: Find total lateral area

There are 4 lateral faces. Total lateral area: \( 4 \times 12 = 48 \, \text{cm}^2 \).

Step4: Find surface area

Surface area = base area + total lateral area: \( 16 + 48 = 64 \, \text{cm}^2 \).

Answer:

\( 64 \)