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 triangular pyramid.

Step2: Find area of the base

The base is a triangle with base - length \(b = 6\) feet and height \(h = 2\) feet. The area of a triangle is \(A_{base}=\frac{1}{2}bh\). So, \(A_{base}=\frac{1}{2}\times6\times2 = 6\) square feet.

Step3: Find area of the three lateral faces

The three lateral - faces are triangles. Two of the lateral faces have base \(b = 5\) feet and height \(h = 2\) feet, and one has base \(b = 6\) feet and height \(h = 2\) feet.
The area of a triangle is \(A=\frac{1}{2}bh\).
For the two congruent lateral faces with \(b = 5\) and \(h = 2\), the combined area is \(2\times\frac{1}{2}\times5\times2=10\) square feet.
For the third lateral face with \(b = 6\) and \(h = 2\), the area is \(\frac{1}{2}\times6\times2 = 6\) square feet.

Step4: Calculate the surface area

The surface area \(SA\) of a triangular pyramid is the sum of the area of the base and the areas of the lateral faces. So, \(SA=A_{base}+A_{lateral}=6 + 10+6=22\) square feet.

Answer:

The solid is a triangular pyramid and its surface area is 22 square feet.