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 placed vertically one on top of the other. All 4 sides of the middle vertical rectangle are drawn with dashed lines. The width of the rectangles is 10 feet. The length of the middle rectangle is 24 feet. Two right triangles adjoin the middle rectangle on the left and right sides, with each base measuring 10 feet and each hypotenuse measuring 26 feet.
Using the net of the triangular prism, what is its surface area?
(1 point)
Responses
1,200 ft.2
1,200 mi. squared
840 ft.2
840 ft. squared
240 ft.2
240 ft. squared
720 ft.2
720 ft. squared
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To find the surface area of the triangular prism, we need to find the area of each of the three rectangles and two triangles.
The area of the middle rectangle is 10 feet (width) * 24 feet (length) = 240 ft^2.
The area of each of the two rectangles adjacent to the middle one is 10 feet (width) * 10 feet (height) = 100 ft^2. Since there are two of these, the total area for both is 200 ft^2.
The area of each triangle is 1/2 * base * height. In this case, the base is 10 feet and the height (hypotenuse) is 26 feet. Therefore, the area of each triangle is 1/2 * 10 feet * 26 feet = 130 ft^2. Since there are two triangles, the total area for both is 260 ft^2.
Adding up all the areas:
240 ft^2 (middle rectangle) + 200 ft^2 (two outer rectangles) + 260 ft^2 (two triangles) = 700 ft^2.
Therefore, the surface area of the triangular prism is 700 ft^2. None of the given responses match this, so the closest option is 720 ft^2.