Josiah wraps a gift box in the shape of a triangular prism. The figure below shows a net for the gift box.On the tactile printout of the following graphs, a is 66 feet, b is 77 feet, c is 55 feet, and d is 7, point, 8, 17.81 feet.
7.81 ft
7.81 ft
6 ft
5 ft
7 ft
6 ft
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How much wrapping paper did he use, in square feet?
To calculate the amount of wrapping paper used, we need to find the surface area of the triangular prism.
The surface area of a triangular prism can be calculated using the formula:
Surface Area = 2 * base area of triangle + lateral area of prism
First, we need to find the base area of the triangle. The base of the triangle is a right triangle with legs of 66 feet and 77 feet.
Base area of triangle = 0.5 * base * height
Base area = 0.5 * 66 * 77 = 2541 square feet
Next, we need to find the lateral area of the prism. The lateral area is the sum of the three rectangles that form the sides of the prism.
Lateral area = (perimeter of base) * height of prism
Perimeter of base = a + b + c = 66 + 77 + 55 = 198 feet
Height of prism = d = 7.81 feet
Lateral area = 198 * 7.81 = 1548.18 square feet
Now, we can calculate the total surface area of the triangular prism:
Surface Area = 2 * base area + lateral area
Surface Area = 2 * 2541 + 1548.18
Surface Area = 5622.36 square feet
Therefore, Josiah used 5622.36 square feet of wrapping paper.