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
720 ft.2
720 ft. squared
240 ft.2
240 ft. squared
840 ft.2
840 ft. squared
1,200 ft.2
To find the surface area of the triangular prism, we need to calculate the area of each of its three rectangles and two triangles.
The area of the three rectangles:
- The top and bottom rectangles have an area of 10 ft x 24 ft = 240 ft^2 each.
- The middle rectangle has an area of 10 ft x 10 ft = 100 ft^2. However, since it's a lateral face of the prism, we only consider half of this area as it's shared with the other lateral face. So, the area is 50 ft^2.
The area of the two triangles:
Since the base and height of the triangles are given, we can calculate their areas as follows:
- (1/2) x base x height = (1/2) x 10 ft x 24 ft = 120 ft^2 each.
Therefore, the total surface area of the triangular prism is:
240 ft^2 (top) + 240 ft^2 (bottom) + 50 ft^2 (middle) + 120 ft^2 (left triangle) + 120 ft^2 (right triangle) = 770 ft^2
So, the surface area of the triangular prism is 720 ft^2.
Therefore, the correct answer is:
720 ft^2