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?
A:240 mi2
B:1,200 mi.
C:840 mi.2
D:720 mi.2
First, we need to find the area of each of the three rectangles by multiplying their length by width. Since they all have the same width of 10 miles, we just need to find the length of each rectangle:
- Top rectangle: 24 x 10 = 240 square miles
- Middle rectangle: 24 x 10 = 240 square miles (only count two sides with dashed lines)
- Bottom rectangle: 10 x 10 = 100 square miles
Next, we need to find the area of each of the two triangles. We can use the formula for the area of a right triangle, which is (base x height) / 2. Since the base of each triangle is 10 miles and the hypotenuse is 26 miles, we can use the Pythagorean theorem to find the height:
- height = sqrt(26^2 - 10^2) = 24 miles (rounded to the nearest mile)
Now we can find the area of each triangle:
- Area of left triangle: (10 x 24) / 2 = 120 square miles
- Area of right triangle: (10 x 24) / 2 = 120 square miles
Finally, we can add up the areas of all the rectangles and triangles to find the total surface area of the triangular prism:
- Total surface area = 240 + 240 + 100 + 120 + 120 = 840 square miles
Therefore, the answer is C: 840 mi.2.