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 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
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To find the surface area of the triangular prism, we need to calculate the areas of all the individual faces and then add them up.
1. The area of the two triangular bases:
Each triangular base has an area of (1/2) * base * height.
Area of one triangle = (1/2) * 8 * 6.9 = 27.6 cm²
Area of both triangles = 2 * 27.6 = 55.2 cm²
2. The lateral surface area of the prism (the three rectangles):
Each rectangle has an area of length * width.
Area of one rectangle = 8 * 6 = 48 cm²
Area of all three rectangles = 3 * 48 = 144 cm²
3. To find the total surface area, we add the area of the two triangles and three rectangles:
Total surface area = 55.2 + 144 = 199.2 cm²
Therefore, the surface area of the triangular prism is 199.2 cm².
The surface area of a triangular prism can be calculated by adding the areas of all its faces.
The lateral surface area of a triangular prism can be calculated by finding the area of the three rectangles and the two triangles.
The area of the rectangles = 3 (width x height) = 3 (6 x 8) = 3 (48) = 144 cm²
The area of the triangles = 2 (base x height)/2 = 2 (8 x 6.9)/2 = 27.6 cm²
Therefore, the lateral surface area of the triangular prism is:
144 + 27.6 = 171.6 cm²
To find the total surface area, we must add the area of the two triangular bases of the prism. Each triangular base has an area of 27.6 cm².
Thus, the total surface area of the triangular prism is:
171.6 + 27.6 + 27.6 = 226.8 cm²
Therefore, the surface area of the triangular prism is 226.8 cm² rounded to the nearest tenth.