First, we need to calculate the area of each triangular end of the prism. We can do this using the formula for the area of a triangle:
Area of triangle = 0.5 x base x height
The height of each end triangle is 9 ft, and the base is half the width, which is 10 ft. To find the length of the other side of the triangle, we can use the Pythagorean theorem: a^2 + b^2 = c^2. In this case, a and b are the two sides of the triangle that we know (9 ft and 10 ft), and c is the hypotenuse of the cover, which is 13.45 ft. Solving for the missing side, we get:
a^2 + b^2 = c^2
9^2 + 10^2 = 13.45^2
81 + 100 = 181.4
sqrt(181.4) = 13.47
So the length of each side of the triangular end is approximately 13.47 ft. Using the formula above, we can find the area of each end:
Area of end triangle = 0.5 x base x height
= 0.5 x 10 ft x 9 ft
= 45 sq ft
To calculate the area of the rectangular sides of the prism, we can use the formula for the area of a rectangle:
Area of rectangle = length x width
The length of the rectangle is 24 ft and the width is 20 ft, so the area of each of the two rectangular sides is:
Area of rectangular side = length x width
= 24 ft x 20 ft
= 480 sq ft
Adding up the areas of the two end triangles and the two rectangular sides, we get the total surface area of the triangular prism tent:
Total surface area = 2 x area of end triangle + 2 x area of rectangular side
= 2 x 45 sq ft + 2 x 480 sq ft
= 90 sq ft + 960 sq ft
= 1050 sq ft
Therefore, the surface area of the triangular prism tent is 1050 square feet.
Calculate the surface area of a triangular prism shaped tent if the height is 9 ft., the length is 24 ft., the width is 20 ft., and the hypotenuse of the cover is 13.45 ft.
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