Question

a box is in the shape of a square prism. the height of the box is 8 inches, and the area of the square base is 16 square inches. what is the total surface area in square inches of the box? a 160 in.² b 128 in.² c 80 in.² d 288 in.²

Explanation:

Step1: Find base side length

Since area of square base is $16$ in.$^2$, side length $s = \sqrt{16} = 4$ inches.

Step2: Calculate lateral surface area

Lateral surface area = perimeter of base $\times$ height. Perimeter = $4s = 4\times4=16$ inches. Lateral area = $16\times8 = 128$ in.$^2$.

Step3: Calculate total surface area

Total surface area = lateral area + $2\times$ base area = $128 + 2\times16$
$=128+32=160$ in.$^2$

Answer:

A. $160$ in.$^2$