se the image to answer the question.
An illustration shows a square pyramid with labeled parts. The left, front, and right faces of the pyramid and base are visible. The back face is not visible, but its position is indicated by a dashed line. The back base edge is not visible, but its position is indicated by a dashed line. The left base edge is labeled a. The back left lateral edge is labeled e. A dotted line extends from the interior of the vertex straight down to the center of the base and is labeled h. A right angle is indicated where the dotted height line meets the base. Another dotted line extends from the center of the base where the height line meets to the center of the right base edge and is labeled r. A dotted line extends from the right base edge straight up the center of the right face of the prism and meets the height line at the vertex. The dotted slant height line is labeled s.
For the square pyramid, the lateral edge length, e , is 25 in., and the slant height, s , is 24 in. Find the height of the pyramid, h . Round the answer to the nearest whole number. Hint: Before finding the length of h , you will first need to find the length of r
.
Based on the description of the image, we can see that the slant height, s, is labeled and given as 24 in. The lateral edge length, e, is also labeled and given as 25 in.
Since the slant height and lateral edge length are both given, we can use the Pythagorean theorem to find the height of the pyramid, h.
We can see that the height of the pyramid, h, is the hypotenuse of a right triangle with the base, r, and the slant height, s, as the other two sides.
Using the Pythagorean theorem:
h^2 = r^2 + s^2
We need to find the length of r.
Looking at the image, we can see that r is the distance from the right base edge to the center of the base. It is labeled and given as a dotted line.
To find the length of r, we can use the fact that the square pyramid is symmetrical. Since the lateral edge length, e, is 25 in, we can find half of e by dividing it by 2.
e/2 = 25/2 = 12.5 in
Therefore, the length of r is 12.5 in.
Now we can substitute the values into the Pythagorean theorem:
h^2 = (12.5)^2 + (24)^2
h^2 = 156.25 + 576
h^2 = 732.25
Taking the square root of both sides:
h = √732.25 ≈ 27 in
So, the height of the pyramid, h, is approximately 27 inches.