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Question

An illustration shows a two-dimensional net of a triangular prism with all of its sides open and visible. The net appears as three horizontal parallelograms joined next to each other. All 4 sides of the middle parallelogram are drawn with dashed lines. The width of the parallelograms is 4 centimeters. The length of the middle parallelogram is 12 centimeters. Two right triangles adjoin the middle parallelogram on the top and bottom 12 centimeter sides, with their hypotenuse sides measuring 15 centimeters and the perpendicular sides measuring 9 centimeters. Right angles are shown at the intersection of the perpendicular sides and the base sides of the triangles.

What is the surface area of the triangular prism whose net is shown?

(1 point)
Responses

216 cm2
216 cm squared

108 cm2
108 cm squared

198 cm2
198 cm squared

252 cm2
252 cm squared
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Answer 1

To find the surface area of the triangular prism, we first need to calculate the area of each individual shape in the net.

1. The area of the middle parallelogram:
Area = length x width
Area = 12 cm x 4 cm
Area = 48 cm^2

2. The area of each right triangle:
Area = 0.5 x base x height
Area = 0.5 x 4 cm x 9 cm
Area = 18 cm^2 (since there are two triangles, the total area of both triangles is 36 cm^2)

Now, add the areas of the middle parallelogram and the two right triangles to find the total surface area of the triangular prism:
48 cm^2 (middle parallelogram) + 36 cm^2 (two triangles) = 84 cm^2

The surface area of the triangular prism whose net is shown is 84 cm^2.