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 miles. The length of the middle rectangle is 24 miles. Two right triangles adjoin the middle rectangle on the left and right sides, with each base measuring 10 miles and each hypotenuse measuring 26 miles.
Using the net of the triangular prism, what is its surface area?
(1 point)
Responses
720 mi.2
720 mi. squared
1,200 mi.2
1,200 mi. squared
840 mi.2
840 mi. squared
240 mi.2
240 mi. squared
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The surface area of a triangular prism can be calculated by finding the sum of the areas of all its faces.
The calculations are as follows:
- The top and bottom faces are rectangles with dimensions 10 miles by 24 miles, so their combined area is 2(10 x 24) = 480 mi^2.
- The two side faces are right triangles with bases of 10 miles and heights of 24 miles, so their combined area is 2(1/2 x 10 x 24) = 240 mi^2.
- The front and back faces are rectangles with dimensions 10 miles by 26 miles, so their combined area is 2(10 x 26) = 520 mi^2.
Therefore, the total surface area of the triangular prism is 480 + 240 + 520 = 1,240 mi^2.
So, the closest answer to our calculations is 1,200 mi^2.