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
252 cm2
252 cm squared
108 cm2
108 cm squared
216 cm2
216 cm squared
198 cm2
198 cm squared
To find the surface area of the triangular prism, we need to calculate the areas of each individual side of the net and then sum them up.
1. Calculate the area of the middle parallelogram:
Area = base x height
Area = 12 cm x 4 cm
Area = 48 cm²
2. Calculate the area of each top and bottom triangle:
Area = 0.5 x base x height
Area = 0.5 x 12 cm x 9 cm
Area = 54 cm² (for each triangle)
3. Calculate the area of the remaining three sides of the triangular prism (the sides not shown in the net):
Area = 4 cm x 15 cm x 3 (there are 3 of these sides since the net only shows three sides repeating)
Area = 180 cm²
4. Add up the areas of all the sides:
48 cm² (middle parallelogram) + 54 cm² (top triangle) + 54 cm² (bottom triangle) + 180 cm² (other sides)
= 336 cm²
The surface area of the triangular prism is 336 cm².