Use the image to answer the 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
108 cm2
108 cm squared
198 cm2
198 cm squared
216 cm2
216 cm squared
252 cm2
252 cm squared
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page 8 of 8
To find the surface area of the triangular prism, we need to calculate the area of each of the three faces: two parallelograms and two triangles.
The area of a parallelogram is base x height. In this case, the base is 12 cm and the height is 4 cm. So, the area of one parallelogram is 12 cm x 4 cm = 48 cm². Since there are two parallelograms, the total area for them is 48 cm² x 2 = 96 cm².
The area of a triangle is given by the formula ½ x base x height. For each triangle, the base is 12 cm and the height is 9 cm. So, the area of one triangle is ½ x 12 cm x 9 cm = 54 cm². Since there are two triangles, the total area for them is 54 cm² x 2 = 108 cm².
Therefore, the total surface area of the triangular prism is 96 cm² (for the parallelograms) + 108 cm² (for the triangles) = 204 cm².
So, the correct answer is not provided in the options given. The closest option to the correct answer would be 198 cm².