Calculate the surface area of a triangular, prism shade tent. If the height is 9 feet, the length is 24 feet, the width is 20 feet in the hypotenuse of the cover is 13.45 feet.(a) 1,215.60ft^2 (b) 1,462.80ft^2
First, calculate the area of the two triangular ends of the prism:
Area of one triangular end = 1/2 * base * height
Area of one triangular end = 1/2 * 24ft * 9ft = 108ft^2
Total area of both triangular ends = 2 * 108ft^2 = 216ft^2
Next, calculate the area of the three rectangular faces of the prism:
Area of one rectangular face = length * width
Area of one rectangular face = 24ft * 20ft = 480ft^2
Total area of three rectangular faces = 3 * 480ft^2 = 1440ft^2
Total surface area of the prism shade tent = Area of both triangular ends + Area of three rectangular faces
Total surface area = 216ft^2 + 1440ft^2 = 1656ft^2
Therefore, the surface area of the triangular prism shade tent is 1,656ft^2.
The closest option to this answer is (b) 1,462.80ft^2.