For the square pyramid, the lateral edge length is 25 in., and the slant height, is 24 in. Find the height of the pyramid. Round the answer to the nearest whole number. The height of the square pyramid is?
To find the height of the pyramid, we can use the Pythagorean theorem.
Let's label the height of the pyramid as "h".
The lateral edge length is given as 25 in., so each side of the base of the pyramid is 25 in.
Since the base is a square, the height of the pyramid would be the same as the height of one of the four triangles that make up the pyramid.
Using the Pythagorean theorem, we can find the height of the triangle:
h^2 = (24^2) - (12.5^2)
h^2 = 576 - 156.25
h^2 = 419.75
Taking the square root of both sides:
h ≈ √419.75
h ≈ 20.49
The height of the pyramid is approximately 20.49 inches, rounded to the nearest whole number. So, the height is 20 inches.
To find the height of the pyramid, we need to use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.
In this case, the lateral edge length is one side of the right triangle, and the slant height is the hypotenuse. Let's call the height of the pyramid "h."
Using the Pythagorean theorem, we can write the equation:
h^2 + (lateral edge length/2)^2 = slant height^2
Substituting the given values into the equation, we have:
h^2 + (25/2)^2 = 24^2
Simplifying:
h^2 + 12.5^2 = 576
h^2 + 156.25 = 576
h^2 = 576 - 156.25
h^2 = 419.75
Taking the square root of both sides gives:
h ≈ √419.75
Rounding to the nearest whole number:
h ≈ 20
Therefore, the height of the square pyramid is approximately 20 inches.
To find the height of the pyramid, we can use the Pythagorean theorem. The theorem states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
In this case, the slant height of the pyramid is the hypotenuse of a right-angled triangle, with the lateral edge length as one of the sides.
Let's call the height of the pyramid "h", the lateral edge length "l", and the slant height "s".
Using the Pythagorean theorem, we can set up the following equation:
s^2 = l^2 + h^2
Plugging in the given values, we have:
24^2 = 25^2 + h^2
Simplifying:
576 = 625 + h^2
Rearranging the equation:
h^2 = 576 - 625
h^2 = -49
Since the equation has a negative value under the square root, it means that there is no real solution for the height of the pyramid. This implies that there might be an error in the given information or problem statement. Please double-check the values provided.