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 horizontal rectangles joined one on top of the other. All 4 sides of the middle rectangle are drawn with dashed lines. The length of the rectangles is 8 meters. The width of all the rectangles is 4 meters. Two identical triangles adjoin the middle rectangle at the left and right with the perpendicular height of the triangles measuring 3.4 meters.
What is the surface area of the triangular prism whose net is shown below? Round the answer to the nearest hundredth.
(1 point)
m2
To find the surface area of the triangular prism, we need to calculate the area of all the individual 5 faces and then add them up.
1. The top and bottom faces are rectangles with dimensions 8m by 4m, so their areas are:
2 * (8m * 4m) = 64m²
2. The front and back faces are also rectangles with dimensions 8m by 3.4m (the height of the triangles), so their areas are:
2 * (8m * 3.4m) = 54.4m²
3. The two triangular faces are identical right triangles with base 8m and height 3.4m. The area of a triangle is 0.5 * base * height, so the area of each triangle is:
0.5 * 8m * 3.4m = 13.6m²
Since there are two triangles, their combined area is:
2 * 13.6m² = 27.2m²
Adding up all the areas, we get:
64m² (top and bottom) + 54.4m² (front and back) + 27.2m² (triangles) = 145.6m²
Therefore, the surface area of the triangular prism is 145.6 square meters.