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. The base is a triangle with base - length 6 feet and height (slant - height of the lateral face) 5 feet, and the lateral faces are triangles with base 5 feet and height 2 feet.

Step2: Calculate the area of the base

The area of a triangle is given by the formula $A_{base}=\frac{1}{2}bh$. For the base triangle with $b = 6$ feet and $h = 5$ feet, $A_{base}=\frac{1}{2}\times6\times5=15$ square feet.

Step3: Calculate the area of the lateral faces

There are 3 lateral faces. Each lateral face has an area $A_{lateral}=\frac{1}{2}bh$. Here, $b = 5$ feet and $h = 2$ feet. So the area of one lateral face is $\frac{1}{2}\times5\times2 = 5$ square feet. The total area of the 3 lateral faces is $3\times5=15$ square feet.

Step4: Calculate the surface area

The surface area $SA$ of the triangular pyramid is the sum of the area of the base and the total area of the lateral faces. So $SA=A_{base}+A_{lateral - total}=15 + 15=30$ square feet.

Answer:

The solid is a triangular pyramid and its surface area is 30 square feet.