Use the image to answer the question.
An illustration shows a triangular prism. The front triangular face is visible. The right rectangular face is visible. The sides and edges that are not visible are indicated by dashed lines. Parts are labeled with measurements. The left side and right side of the triangle measure 17 meters. The perpendicular height from the top vertex of the triangle to the base measures 15 meters. The base of the triangle measures 16 meters. The width of the rectangular face measures 11 meters.
What is the surface area of the net of the triangular prism?
(1 point)
Responses
768 square meters
768 square meters
779 square meters
779 square meters
790 square meters
790 square meters
822 square meters
822 square meters
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Given the dimensions provided, we can calculate the surface area of the net of the triangular prism as follows:
Surface Area = 2(base area of the triangular face) + (perimeter of the triangular face) * (width of the rectangular face) + (base perimeter of the triangular face) * (height of the prism)
Base area of the triangular face = (1/2) * height * base
Base area of the triangular face = (1/2) * 15 * 16 = 120 square meters
Perimeter of the triangular face = 17 + 17 + 16 = 50 meters
Base perimeter of the triangular face = 16 + 16 + 17 + 17 = 66 meters
Surface Area = 2(120) + 50 * 11 + 66 * 11
Surface Area = 240 + 550 + 726
Surface Area = 1516 square meters
Therefore, the surface area of the net of the triangular prism is 1516 square meters. None of the provided options match the calculated answer, so the closest option is 779 square meters.
are you sure?
I apologize for the error in my calculations. Let me correct it:
Surface Area = 2(base area of the triangular face) + (perimeter of the triangular face) * (width of the rectangular face) + (base perimeter of the triangular face) * (height of the prism)
Base area of the triangular face = (1/2) * height * base
Base area of the triangular face = (1/2) * 15 * 16 = 120 square meters
Perimeter of the triangular face = 17 + 17 + 16 = 50 meters
Base perimeter of the triangular face = 16 + 16 + 17 = 50 meters
Surface Area = 2(120) + 50 * 11 + 50 * 11
Surface Area = 240 + 550 + 550
Surface Area = 1340 square meters
Therefore, the surface area of the net of the triangular prism is 1340 square meters. None of the options provided match the calculated answer. I apologize for the oversight in my initial response.