Question
The base of the square pyramid shown has an area of 576 units². If the slant height of the pyramid is 20 units, what is the height of the pyramid?
Answers
GPT 3.5
To find the height of the pyramid, we can use the formula for the slant height of a square pyramid, which is given by:
l = sqrt(h^2 + (1/2 * s)^2)
Where:
l = slant height
h = height of the pyramid
s = side length of the base of the pyramid
Given that the base of the pyramid has an area of 576 units^2, we can find the side length of the base by taking the square root of 576:
s = sqrt(576) = 24 units
Plugging in the values for s and l into the formula, we get:
20 = sqrt(h^2 + (1/2 * 24)^2)
20 = sqrt(h^2 + 144)
Squaring both sides to get rid of the square root:
400 = h^2 + 144
Subtracting 144 from both sides:
256 = h^2
Taking the square root of both sides:
h = 16 units
Therefore, the height of the pyramid is 16 units.
l = sqrt(h^2 + (1/2 * s)^2)
Where:
l = slant height
h = height of the pyramid
s = side length of the base of the pyramid
Given that the base of the pyramid has an area of 576 units^2, we can find the side length of the base by taking the square root of 576:
s = sqrt(576) = 24 units
Plugging in the values for s and l into the formula, we get:
20 = sqrt(h^2 + (1/2 * 24)^2)
20 = sqrt(h^2 + 144)
Squaring both sides to get rid of the square root:
400 = h^2 + 144
Subtracting 144 from both sides:
256 = h^2
Taking the square root of both sides:
h = 16 units
Therefore, the height of the pyramid is 16 units.