the square pyramid the lateral edge length is 25in. and the slant height is 24in. Find the height of the pyramid Round the answer to the nearest whole number. what is the height of the pyramid?
To find the height of the square pyramid, we can use the Pythagorean Theorem. The Pythagorean Theorem states that in a right 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 (24 in) is the hypotenuse, and one-half of the base of the pyramid (which is also the lateral edge length divided by 2) is one of the other sides. Let's call the height of the pyramid "h".
Using the Pythagorean Theorem, we can set up the equation:
(0.5 x Lateral Edge Length)^2 + h^2 = Slant Height^2
Now we can substitute in the given values:
(0.5 x 25 in)^2 + h^2 = 24 in^2
Simplifying further:
(12.5 in)^2 + h^2 = 24 in^2
156.25 in^2 + h^2 = 576 in^2
Now, we can isolate the variable "h":
h^2 = 576 in^2 - 156.25 in^2
h^2 = 419.75 in^2
To find "h", we take the square root of both sides:
h = √(419.75 in^2)
Using a calculator, we find:
h ≈ 20.49 in
Rounding to the nearest whole number, the height of the pyramid is:
h ≈ 20 in
To find the height of the square pyramid, we can use the Pythagorean theorem.
The lateral edge length of the square pyramid is given as 25 inches, and the slant height is given as 24 inches.
Let's label the height of the pyramid as 'h'.
Using the Pythagorean theorem, we have:
(lateral edge length)^2 = (height)^2 + (slant height)^2
Substituting the given values:
25^2 = h^2 + 24^2
625 = h^2 + 576
Rearranging the equation:
h^2 = 625 - 576
h^2 = 49
Taking the square root of both sides:
h ≈ √49
h ≈ 7
Therefore, the height of the pyramid is approximately 7 inches (rounded to the nearest whole number).
To find the height of the pyramid, we can use the Pythagorean theorem.
Let's denote the height of the pyramid as "h".
According to the given information, the lateral edge length is 25in. This means that the base of the pyramid is a square with side length 25in.
Furthermore, the slant height of the pyramid is given as 24in.
Using the Pythagorean theorem, we can establish the following equation:
h^2 + (25/2)^2 = 24^2
Simplifying this equation, we have:
h^2 + 625/4 = 576
Multiplying both sides of the equation by 4 to eliminate the fraction, we get:
4h^2 + 625 = 2304
Subtracting 625 from both sides of the equation, we obtain:
4h^2 = 1679
Dividing both sides of the equation by 4, we have:
h^2 = 1679/4
Taking the square root of both sides of the equation, we get:
h ≈ 20.47
Rounding the answer to the nearest whole number, the height of the pyramid is approximately 20 inches.