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Question

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

97.24 cm2
97.24 cm squared

603.16 cm2
603.16 cm squared

700.40 cm2
700.40 cm squared

573.24 cm2
573.24 cm squared
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Answer 1

The surface area of the triangular prism can be calculated by finding the area of each of the five faces and then adding them together.

1. Area of the rectangular base: 17 cm x 13 cm = 221 cm^2 (there are two of these faces)

2. Area of the triangular faces: (1/2) x base x height
- Front triangle: (1/2) x 13 cm x 7.48 cm = 48.74 cm^2
- Back triangle (which is congruent to the front triangle): 48.74 cm^2

3. Area of the rectangular side faces: length x height
- 17 cm x 15 cm = 255 cm^2 (there are two of these faces)

Total surface area = 2(221 cm^2) + 2(48.74 cm^2) + 2(255 cm^2)
= 442 cm^2 + 97.48 cm^2 + 510 cm^2
= 573.24 cm^2

Therefore, the surface area of the triangular prism is 573.24 cm^2.