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.
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?
1 answer