Question

what is the surface area of the right triangular prism? show your work.

Explanation:

Step1: Find area of triangular faces

The formula for the area of a triangle is $A=\frac{1}{2}bh$. For the right - angled triangle with base $b = 16$ ft and height $h = 15$ ft, $A_{triangle}=\frac{1}{2}\times16\times15=120$ square feet. Since there are 2 triangular faces, the total area of triangular faces is $2\times120 = 240$ square feet.

Step2: Find area of rectangular faces

There are 3 rectangular faces.
Face 1: With dimensions 16 ft and 25 ft, $A_1=16\times25 = 400$ square feet.
Face 2: With dimensions 15 ft and 25 ft, $A_2=15\times25 = 375$ square feet.
Face 3: With dimensions 20 ft and 25 ft, $A_3=20\times25 = 500$ square feet.
The total area of rectangular faces is $A_{rectangles}=400 + 375+500=1275$ square feet.

Step3: Calculate total surface area

The surface area $S$ of the triangular prism is the sum of the area of the triangular faces and the area of the rectangular faces. So $S=240 + 1275=1515$ square feet.

Answer:

1515 square feet