The net shown represents a square pyramid. 20 ft 32 ft Determine the area, in square feet, of one triangular face of the square pyramid.
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To find the area of one triangular face of the square pyramid, we first need to determine the length of the base and the height of the triangular face.
The net provided shows a square pyramid with dimensions of 20 ft and 32 ft. Since it is a square pyramid, the base is a square, and both sides of the square have the same length.
From the given dimensions, we can determine that the length of each side of the square base is 20 ft.
Next, we need to find the height of the triangular face. In a square pyramid, the height represents the distance between the apex (the top of the pyramid) and the center of the square base.
Since we only have the dimensions of the square base, we need to use trigonometry to calculate the height. Let's assume H is the height of the triangular face.
Using Pythagoras' theorem, we can write:
(H/2)^2 + 20^2 = 32^2
Simplifying the equation:
(H^2/4) + 400 = 1024
H^2/4 = 624
H^2 = 2496
H ≈ 49.96 ft (rounded to two decimal places)
Now that we have the length of the base (20 ft) and the height (approximately 49.96 ft), we can calculate the area of one triangular face using the formula for the area of a triangle:
Area = (base * height) / 2
Area = (20 ft * 49.96 ft) / 2
Area ≈ 498.20 square feet (rounded to two decimal places)
Therefore, the area of one triangular face of the square pyramid is approximately 498.20 square feet.