Question

lesson 3 finding the surface area of three - dimensional figure 7

Explanation:

Step1: Calculate base area

The base is a square with side - length $s = 8$ ft. The area of a square is $A_{base}=s^{2}$. So, $A_{base}=8^{2}=64$ square feet.

Step2: Calculate area of one triangular face

The formula for the area of a triangle is $A=\frac{1}{2}bh$. For the triangular faces of the pyramid, the base $b = 8$ ft and the height $h = 9.2$ ft. So, the area of one triangular face $A_{triangle}=\frac{1}{2}\times8\times9.2 = 36.8$ square feet.

Step3: Calculate total area of triangular faces

Since there are 4 triangular faces, the total area of the triangular faces $A_{triangles}=4\times A_{triangle}=4\times36.8 = 147.2$ square feet.

Step4: Calculate surface area of the pyramid

The surface area $SA$ of a square - based pyramid is the sum of the base area and the total area of the triangular faces. So, $SA=A_{base}+A_{triangles}=64 + 147.2=211.2$ square feet.

Answer:

$211.2$ square feet