Surface Area of Triangular Prisms Practice
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Question
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An illustration shows a two-dimensional net of a triangular prism with all of its sides open and visible. The net appears as three vertical rectangles joined next to each other. All 4 sides of the middle rectangle are drawn with dashed lines. The width of the rectangles is 6 centimeters. The length of the middle rectangle is 8 centimeters. Two identical triangles adjoin the middle rectangle at the top and bottom with sides each measuring 8 centimeters and the perpendicular height measuring 6.9 centimeters.
What is the surface area of the triangular prism? Round the answer to the nearest tenth.
(1 point)
cm2
To find the surface area of the triangular prism, we need to calculate the area of each individual face and then sum them up.
1. The area of the middle rectangle (front and back face):
Area = length x width = 8 cm x 6 cm = 48 cm²
Both the front and back face have the same area, so the total area for both is 2 x 48 cm² = 96 cm²
2. The area of the two triangles (top and bottom face):
Area = 1/2 x base x height = 1/2 x 8 cm x 6.9 cm = 27.6 cm²
Both the top and bottom face have the same area, so the total area for both is 2 x 27.6 cm² = 55.2 cm²
3. Finally, add all three areas together to get the total surface area of the triangular prism:
Surface Area = 96 cm² (middle rectangle) + 55.2 cm² (triangles) = 151.2 cm²
Therefore, the surface area of the triangular prism is 151.2 cm² (rounded to the nearest tenth).