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 net represents a square - based pyramid. The base is a square with side length \(s = 6\) feet and the slant height \(l=7\) feet.

Step2: Calculate the area of the base

The area of the square base \(B\) is given by the formula \(B=s^{2}\), where \(s = 6\). So \(B = 6^{2}=36\) square feet.

Step3: Calculate the area of one triangular face

The area of a triangle is \(A_{\triangle}=\frac{1}{2}sl\), where \(s\) is the base of the triangle (equal to the side - length of the square base) and \(l\) is the slant height. Here, \(s = 6\) and \(l = 7\), so \(A_{\triangle}=\frac{1}{2}\times6\times7 = 21\) square feet.

Step4: Calculate the total surface area

A square - based pyramid has 4 triangular faces and 1 square base. The total surface area \(SA\) is \(SA=B + 4A_{\triangle}\). Substitute \(B = 36\) and \(A_{\triangle}=21\) into the formula: \(SA=36+4\times21=36 + 84=120\) square feet.

Answer:

The solid is a square - based pyramid and its surface area is 120 square feet.