Question

Use a net to find the surface area of the right triangular prism shown below: Three rectangles next to each other with a width of 10 feet. The first and second rectangles length are unknown, and the last is 15 feet long. There are two right triangles above and below the last rectangle. One is labeled with a base of 9 feet and a height of 12 feet.

104 square feet
412 square feet
468 square feet
504 square feet

Answer 1

Solution:

Surface Area of Right triangular prism =

        Area of Upper and lower part  which is in the shape of right triangle with a base of 9 feet and a height of 12 feet + Area of three rectangles (first having  length 15 feet and width 10 feet+ Second having length 12 feet and width 10 feet+ Third having  length 9 feet and width 10 feet)

$=\frac{1}{2}\times 2\times 12 \times 9 +15 \times 10 + 12 \times 10 + 9 \times 10\\\\ = 108 + 150 +120 +90\\\\ = 468$

Option (C) 468 square feet = Surface Area of right triangular prism

Answer 2

The surface area of the right triangular prism = 360 + 108 = 468 sq. ft. (Option C).

What is the Surface Area of a Right triangular prism?

Using the net given, the surface area of a right triangular prism = area of 3 rectangular faces + area of the two right triangular faces.

Area of rectangle = length × width

Area of triangle = 1/2(base × height)

Area of the 3 rectangular faces = (10 × 15) + (10 × 12) + (10 × 9) = 360 sq. ft.

Area of the two right triangles = 2[1/2(9 × 12)] = 108 sq. ft.

Therefore, the surface area of the right triangular prism = 360 + 108 = 468 sq. ft. (Option C).

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