Question

identify the solid that is represented by the net. then find its surface area. (all lengths are in feet.)

Explanation:

Step1: Identify the solid

The solid is a square - based pyramid. The base is a square with side length $s = 6$ feet and the slant height $l=6.7$ feet.

Step2: Calculate the area of the base

The area of the square base $B$ is given by the formula $B=s^{2}$. Substituting $s = 6$ feet, we get $B = 6^{2}=36$ square - feet.

Step3: Calculate the area of the four triangular faces

The area of a single triangular face of a pyramid is given by $A_{triangle}=\frac{1}{2}sl$, where $s$ is the base of the triangle (side - length of the square base) and $l$ is the slant height. Substituting $s = 6$ feet and $l = 6.7$ feet, we get $A_{triangle}=\frac{1}{2}\times6\times6.7 = 20.1$ square - feet. The area of the four triangular faces $A_{triangles}=4\times A_{triangle}=4\times20.1 = 80.4$ square - feet.

Step4: Calculate the surface area

The surface area $SA$ of a square - based pyramid is the sum of the area of the base and the area of the four triangular faces. So, $SA=B + A_{triangles}=36+80.4 = 116.4$ square - feet.

Answer:

The solid is a square - based pyramid and its surface area is 116.4 square feet.