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An illustration shows a triangular prism placed sideways with one of its rectangular faces as the base. Dimensions are labeled. The length and width of the rectangular base are 17 centimeters and 13 centimeters respectively. The face visible in front appears as a triangle. The base width of the triangle is 13 centimeters. The perpendicular leg of the triangle is 7.48 centimeters and the slanting leg (hypotenuse) is 15 centimeters. The edges that are not visible are represented by dashed lines.
Apply the technique of using nets to find the surface area of this triangular prism. Your answer should have two decimal places.
(1 point)
Responses
573.24 cm2
573.24 cm squared
603.16 cm2
603.16 cm squared
700.40 cm2
700.40 cm squared
97.24 cm2
97.24 cm squared
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To find the surface area of the triangular prism using the net, we need to find the areas of each individual face and then add them all up.
1. The area of the rectangular base:
Area = length x width
Area = 17 cm x 13 cm
Area = 221 cm2
2. The area of the triangle front face:
Since the base width is 13 cm and the perpendicular leg is 7.48 cm, we can calculate the area of the triangle using the formula for the area of a triangle: 1/2 x base x height.
Area = 1/2 x 13 cm x 7.48 cm
Area = 48.74 cm2
3. The areas of the side faces can be found by calculating the area of each rectangle formed when the net of the prism is unfolded. Both rectangles have the same dimensions as the base rectangle. So, each rectangle's area is 221 cm2.
Now, total surface area = 2 x (area of the base) + (area of the front face) + 2 x (area of the side face)
Total surface area = 2 x 221 cm2 + 48.74 cm2 + 2 x 221 cm2
Total surface area = 442 cm2 + 48.74 cm2 + 442 cm2
Total surface area = 932.74 cm2
Therefore, the surface area of this triangular prism is 932.74 cm2. This answer has been rounded to two decimal places.