Question

1. what is the surface area of the three - dimensional figure represented by this net? work: 3×8 = 24 3×8 = 24 3×8 = 24 3×8 = 24 3×8 = +24 96 + 9 105 square inches 105 6.g.a.4

Explanation:

Step1: Identify the shapes in the net

The net consists of a square base and 4 congruent triangles.

Step2: Calculate the area of the square base

The side - length of the square base is 3 inches. The area of a square is $A = s^2$, so $A_{base}=3\times3 = 9$ square inches.

Step3: Calculate the area of one triangle

The base of each triangle is 3 inches and the height is 8 inches. The area of a triangle is $A=\frac{1}{2}bh$, so $A_{triangle}=\frac{1}{2}\times3\times8=12$ square inches.

Step4: Calculate the total area of the 4 triangles

Since there are 4 congruent triangles, $A_{triangles\ total}=4\times A_{triangle}=4\times12 = 48$ square inches.

Step5: Calculate the surface area of the 3 - D figure

The surface area $SA$ is the sum of the area of the base and the area of the 4 triangles. So $SA=A_{base}+A_{triangles\ total}=9 + 48=105$ square inches.

Answer:

105 square inches