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
240 mi.2
240 mi. squared
840 mi.2
840 mi. squared
1,200 mi.2
1,200 mi. squared
720 mi.2
The surface area of a prism can be calculated by adding the areas of all its faces.
In this case, the triangular prism has 3 rectangular faces and 2 triangular faces. The area of each rectangular face is length x width, so the total area of the 3 rectangular faces is 3 x (24 x 10) = 720 mi^2.
The area of one of the triangular faces can be calculated as (1/2) x base x height, which is (1/2) x 10 x 26 = 130 mi^2. Since there are 2 triangular faces, the total area of the triangular faces is 2 x 130 = 260 mi^2.
Therefore, the total surface area of the triangular prism is 720 (rectangular faces) + 260 (triangular faces) = 980 mi^2.
So, the correct option is: 720 mi^2