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
216 cm2
216 cm squared
252 cm2
252 cm squared
108 cm2
108 cm squared
198 cm2
198 cm squared
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To find the surface area of the triangular prism, we calculate the area of each shape in the net and then sum them up.
The area of the middle parallelogram can be found using the formula for the area of a parallelogram, which is base x height. In this case, the base is 12 cm (the length) and the height is 4 cm (the width), so the area is 12 x 4 = 48 cm².
The area of the two triangles can be found using the formula for the area of a triangle, which is 1/2 x base x height. In this case, the base and height are 9 cm and 12 cm, so the area of each triangle is 1/2 x 9 x 12 = 54 cm². Since there are two triangles, the total area for the triangles is 54 + 54 = 108 cm².
Now, we sum up the areas of the middle parallelogram and the two triangles to find the total surface area of the triangular prism: 48 cm² (parallelogram) + 108 cm² (triangles) = 156 cm².
Therefore, the surface area of the triangular prism whose net is shown is 156 cm². So, the closest option is 198 cm².