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
198 cm2
, 198 cm squared
216 cm2
, , 216 cm squared
252 cm2
252 cm squared
108 cm2
To find the surface area of the triangular prism, we need to add up the areas of all its faces.
First, the middle parallelogram has a length of 12 cm and a width of 4 cm, so its area is 12 x 4 = 48 cm^2.
There are two identical triangles on each end of the prism. Each triangle has a base of 12 cm and a height of 9 cm, so its area is 1/2 x 12 x 9 = 54 cm^2. Since there are two triangles, the total area of the two triangles is 2 x 54 = 108 cm^2.
To find the total surface area, we add up the areas of the three faces: 48 cm^2 for the middle parallelogram plus 108 cm^2 for the two triangles on the ends, giving us a total surface area of 48 + 108 = 156 cm^2.
However, we need to remember that a triangular prism has two congruent parallel faces (the top and bottom faces in this case), so we need to double our result to get the final answer:
156 x 2 = 312 cm^2
Therefore, the surface area of the triangular prism is 312 cm^2.
Answer: 312 cm^2.