Question
The lateral area of a pyramid with a square base is 240 ft squared. Its base edges are 12ft long. Find the height of the pyramid
Answers
GPT 3.5
Let the height of the pyramid be h.
Since the base of the pyramid is a square with sides of length 12 ft, the area of the base is 12^2 = 144 ft^2.
The lateral area of a pyramid is given by the formula A = 1/2 * P * h, where P is the perimeter of the base and h is the height of the pyramid.
Since the base is a square, the perimeter of the base is 4 times the length of one side: P = 4 * 12 = 48 ft.
Given that the lateral area is 240 ft^2, we can write:
240 = 1/2 * 48 * h
Solving for h:
240 = 24h
h = 240 / 24
h = 10 ft
Therefore, the height of the pyramid is 10 ft.
Since the base of the pyramid is a square with sides of length 12 ft, the area of the base is 12^2 = 144 ft^2.
The lateral area of a pyramid is given by the formula A = 1/2 * P * h, where P is the perimeter of the base and h is the height of the pyramid.
Since the base is a square, the perimeter of the base is 4 times the length of one side: P = 4 * 12 = 48 ft.
Given that the lateral area is 240 ft^2, we can write:
240 = 1/2 * 48 * h
Solving for h:
240 = 24h
h = 240 / 24
h = 10 ft
Therefore, the height of the pyramid is 10 ft.