Solar innovations, make a skylight in the shape of a square pyramid. The pyramid is represented with the net how many square feet of acrylic are needed to make a skylight covering the lateral surface area.
20 feet
40 feet
40 feet
40 feet
40 feet
To calculate the lateral surface area of a square pyramid, we first need to determine the slant height of the pyramid. The slant height can be found using the Pythagorean theorem with half the base length and the slant height.
Let's assume the base of the square pyramid is 40 feet (as given in the question). Since it is a square pyramid, the base length is the same as the base width.
Base length = Base width = 40 feet
Half of the base length = 40/2 = 20 feet
Using the Pythagorean theorem, we can find the slant height (l):
l^2 = (20)^2 + (20)^2
l^2 = 400 + 400
l^2 = 800
l ≈ 28.28 feet (approx.)
To find the lateral surface area of the square pyramid, we use the formula:
Lateral Surface Area = Perimeter of base x slant height / 2
Perimeter of base = 4 x base length
Perimeter of base = 4 x 40
Perimeter of base = 160 feet
Lateral Surface Area = 160 x 28.28 / 2
Lateral Surface Area ≈ 2262.4 square feet
Therefore, approximately 2262.4 square feet of acrylic are needed to make the skylight covering the lateral surface area of the square pyramid.