Answer:
144.53 square feet
Explanation:
You want the total surface area of a rectangular pyramid with base dimensions 7 ft by 6 ft and face slant heights of 7.79 ft and 8 ft.
Surface area
The surface area of the pyramid is the sum of the areas of the triangular faces and the area of the base.
Face area
The area of each triangular face is given by ...
A = 1/2bh
There are two faces of each dimension, so the lateral area will be ...
LA = (7 ft)(7.79 ft) +(6 ft)(8 ft) = 102.53 ft²
Base area
The base area will be the product of the rectangle dimensions:
B = LW
B = (7 ft)(6 ft) = 42 ft²
Total area
Then the total surface area is 102.53 ft² +42 ft² = 144.53 ft².
The area of glass needed to cover the entire pyramid is 144.53 ft².
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Additional comment
The triangular face on the long side will have a shorter slant height, since the base of that triangle is closer to the center of the pyramid.
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