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 one on top of the other. All 4 sides of the middle rectangle are drawn with dashed lines. The width of the rectangles is 7 millimeters. The length of the middle rectangle is 8 millimeters. Two right triangles adjoin the middle rectangle on the left and the right, with the perpendicular sides measuring 6 millimeters and the hypotenuse measuring 10 millimeters.
Using the net of the prism shown, what is its surface area?
(1 point)
mm2
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To find the surface area of the prism, we need to calculate the area of each individual face and then add them all together.
1. The middle rectangle has a length of 8 mm and a width of 7 mm, so its area is 8 mm * 7 mm = 56 mm².
2. The two rectangles on the side have a length of 10 mm (the hypotenuse of the right triangles) and a width of 7 mm, so the area of each side rectangle is 10 mm * 7 mm = 70 mm².
3. The two right triangles have a base of 6 mm and height of 8 mm (the length of the middle rectangle). The area of each triangle is 1/2 * base * height = 1/2 * 6 mm * 8 mm = 24 mm².
Now, add up the area of all the faces:
- Middle rectangle: 56 mm²
- Two side rectangles: 2 * 70 mm² = 140 mm²
- Two right triangles: 2 * 24 mm² = 48 mm²
Total surface area = 56 mm² + 140 mm² + 48 mm² = 244 mm²
Therefore, the surface area of the triangular prism is 244 mm².