Question

What is the surfacearea, in square inches,of the square pyramidbelow?

Answer 1

hi, for solve this question we need to use the formula below:

$\text{Area of each triangle + area of the quadrangular base = Total area}$

First, the area of the base:

$\begin{gathered} \text{area base = side }\cdot\text{ side} \\ \text{area base = 4in }\cdot\text{ 4in} \\ \text{area base = 16in}^2 \end{gathered}$

Now, the area of each triangular side:

we have the base as 4in, and the height as 9in.

So, using the formula:

$\begin{gathered} \text{area = }\frac{\text{ base }\cdot\text{ height}}{2} \\ \text{area = }\frac{\text{ 4 }\cdot9}{2} \\ \text{area = }\frac{\text{3}6}{2}=18in^2\text{ each triangular side} \end{gathered}$

Now, let's sum all of the values:

4 triangular sides + 1 quadrangular side

(4 * 18in) + (1 * 16in)

72in² + 16in² = 88in²

Answer: ALTERNATIVE NUMBER 2. 88in²