Question

8 find the surface area of the figure below: gina wilson (all things algebra), 2014

Explanation:

Step1: Identify the figure

The figure is a triangular - prism.

Step2: Find the area of the triangular bases

The base of the triangle has a base length $b = 3$ ft and height $h = 3.7$ ft. The area of a triangle is $A_{triangle}=\frac{1}{2}bh$.
$A_{triangle}=\frac{1}{2}\times3\times3.7=\frac{11.1}{2}=5.55$ square - feet. Since there are 2 triangular bases, the total area of the bases is $2\times5.55 = 11.1$ square - feet.

Step3: Find the area of the rectangular faces

There are 3 rectangular faces.
Face 1: Dimensions $4$ ft by $3$ ft, area $A_1 = 4\times3=12$ square - feet.
Face 2: Dimensions $4$ ft by $9$ ft, area $A_2 = 4\times9 = 36$ square - feet.
Face 3: Dimensions $4$ ft by $6$ ft, area $A_3 = 4\times6=24$ square - feet.
The total area of the rectangular faces is $A_{rectangles}=12 + 36+24=72$ square - feet.

Step4: Calculate the surface area

The surface area $A$ of the triangular prism is the sum of the area of the bases and the area of the rectangular faces.
$A=11.1 + 72=83.1$ square - feet.

Answer:

$83.1$ square feet