A triangular prism. The rectangular sides are 3 feet by 2 feet, 3 feet by 2.5 feet, and 3 feet by 1.5 feet. The 2 triangular sides have a base of 2 feet and height of 1.5 feet.

Trenton is building a skateboarding ramp in the shape of a triangular prism. According to his plan, the ramp would have a base of 2 feet, a height of 1.5 feet, and a length of 3 feet. The riding surface would measure 2.5 feet.

If Trenton wants to cover all faces of the ramp with plywood, how much plywood will he need to buy?

Trenton will need
square feet of plywood.

Total surface area of a triangular prism = (perimeter of triangular base × length of prism) + 2(area of triangular base) = (s1 + s2 + s3 × L) + 2(1/2 × b ×h).

The amount of plywood needed to cover the ramp = total surface area of the triangular prism-shaped ramp.

We are given the parameters:

s1 = 2 ft
s2 = 1.5 ft
s3 = 2.5
L = 3 ft
b = 2 ft
h = 1.5 ft

Total surface area of the triangular prism-shaped ramp = (s1 + s2 + s3)L + 2(1/2 × b ×h) = (2 + 1.5 + 2.5)3 + 2(1/2 × 2 ×1.5)

= (18) + (3)

Total surface area = 21 ft²

Trenton will need 21 square feet of plywood.

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