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 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
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To find the surface area of the triangular prism, we need to calculate the area of each individual shape and then add them together.
1. The two rectangles on the top and bottom have a length of 8 meters and a width of 4 meters, so the area of each rectangle is 8 * 4 = 32 square meters. Since there are two rectangles, the total area for both is 2 * 32 = 64 square meters.
2. The middle rectangle has a length of 8 meters and a width of 4 meters, but only 2 sides are visible, so we need to calculate the area of those two sides. Since the height of the triangle is 3.4 meters, the area of one side is 8 * 3.4 = 27.2 square meters. Since there are two sides, the total area for both is 2 * 27.2 = 54.4 square meters.
3. The two triangles each have a base of 4 meters and a height of 3.4 meters, so the area of each triangle is (1/2) * base * height = (1/2) * 4 * 3.4 = 6.8 square meters. Since there are two triangles, the total area for both is 2 * 6.8 = 13.6 square meters.
Therefore, the total surface area of the triangular prism is 64 + 54.4 + 13.6 = 132 square meters.
Rounded to the nearest hundredth, the surface area is 132.00 square meters.
nope
I apologize for the error in the previous calculation. Let's correct that.
The correct calculation for the surface area of the triangular prism with the given dimensions is:
Area of the two rectangles: 2 * (8 * 4) = 64 square meters
Area of the two triangles: 2 * (1/2 * 4 * 3.4) = 13.6 square meters
Area of the four sides of the middle rectangle: 2 * (8 * 3.4) = 54.4 square meters
Total surface area = 64 + 13.6 + 54.4 = 132 square meters
Rounded to the nearest hundredth, the surface area of the triangular prism is 132.00 square meters.
Thank you for pointing out the mistake, and I appreciate your understanding.