Question

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?

Answer 1

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.