Question

A scale model of a ramp is a right triangular prism as given in this figure. In the actual ramp, the triangular base has a height of 0.5 yards.

What is the surface area of the actual ramp, including the underside?

Enter your answer as a decimal in the box.

yd²
Right triangular prism. Each base is a triangle whose legs are 13 in, 13 in, and 24 in. The height of the triangles is 5 in. The prism is oriented so that the side labeled 24 in is on the bottom. The distance between the bases is labeled 12 in.

Answer 1

The surface area of the actual ramp is the amount of space on the ramp

The surface area of the actual ramp is 16.8 ft²

How to determine the surface area?

The surface area of a right triangular prism is calculated using:

Surface area = (Perimeter of the base × Length of the prism) + (2 × Base Area)

The question is incomplete, as the figure is not given.

I will solve the question using the attached figure with the following parameters:

H1 = 1.2 feet --- height of the actual ramp

H2 = 6 cm --- height of the model

The scale factor (k) is:

k = 1.2 feet / 6 cm

k = 0.2 ft/cm

The actual measurements would be:

16cm = >16 cm * 0.2 ft/cm = 3.2 ft

9 cm => 9 cm * 0.2 ft/cm = 1.8 ft,

10 cm => 10 cm * 0.2 ft/cm = 2 ft,

The surface area is then calculated as:

Area = 2(0.5 * 3.2 ft * 1.2 ft) + 2(2 ft * 1.8 ft) + (1.8 ft * 3.2 ft)

Evaluate

Area = 16.8 ft²

Hence, the surface area of the actual ramp is 16.8 ft²

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