Question

16 in
11 in
Show work!

Answer 1

473 in²

Explanation:

The surface area of a square-based pyramid consists of the square base and four congruent triangular faces.

Area of the square base

The square base of the given pyramid has a side length of 11 inches.

To find its area, simply square the side length (s):

`\begin{aligned}\textsf{Area of the square base}&=\sf s^2\\&=\sf (11\; in)^2\\&=\sf 121\;in^2\end{aligned}`

Area of a triangular face

The area of a triangle is half the product of its base and height.

Given the base of the triangle is equal to the side length of the square base (11 inches), and the height of the triangle is 16 inches:

`\begin{aligned}\textsf{Area of a triangular face}&=\sf (1)/(2)* base * height\\\\&=\sf (1)/(2) * 11\;in * 16\; in\\\\&=\sf 88\;in^2\end{aligned}`

Total surface area

To find the total surface area, add the area of the square base and the combined area of the four triangular faces:

`\begin{aligned}\textsf{Total surface area}&=\sf Area_(base)+4 * Area_(triangle)\\\\&=\sf 121\; in^2+4 * 88\;in^2\\\\&=\sf 121\; in^2+352\;in^2\\\\&=\sf 473\; in^2\end{aligned}`

So, the total surface area of the square-based pyramid is 473 square inches.