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
.
(1 point)
The height of the square pyramid is
in.
To find the height of the square pyramid, we need to find the length of r first.
From the given information, we know that the slant height (s) is 24 inches. Since the slant height and the lateral edge length (e) form a right triangle, we can use the Pythagorean theorem to find the length of r.
Using the Pythagorean theorem:
r^2 + s^2 = e^2
r^2 + 24^2 = 25^2
r^2 + 576 = 625
r^2 = 625 - 576
r^2 = 49
r = √49
r = 7 inches
Now that we have the length of r, we can use it to find the height (h) of the pyramid. From the figure, we can see that the height line (h) forms a right triangle with the base and the slant height.
Using the Pythagorean theorem:
h^2 + r^2 = s^2
h^2 + 7^2 = 24^2
h^2 + 49 = 576
h^2 = 576 - 49
h^2 = 527
h = √527
h ≈ 22 inches
Therefore, the height of the square pyramid is approximately 22 inches.
nah
I apologize for any confusion. Let me try solving the problem again.
Given:
Lateral edge length (e) = 25 in
Slant height (s) = 24 in
To find the height of the pyramid (h), we need to find the length of r first.
Using the Pythagorean theorem:
r^2 + s^2 = e^2
r^2 + 24^2 = 25^2
r^2 + 576 = 625
r^2 = 625 - 576
r^2 = 49
r = √49
r = 7 in
Now that we have the length of r, we can find the height (h) of the pyramid. From the figure, we see that the height line (h) is perpendicular to the base, forming a right triangle with the slant height (s) as the hypotenuse.
Using the Pythagorean theorem:
h^2 + r^2 = s^2
h^2 + 7^2 = 24^2
h^2 + 49 = 576
h^2 = 576 - 49
h^2 = 527
h = √527
h ≈ 22.94 inches
Therefore, rounding the answer to the nearest whole number, the height of the square pyramid is approximately 23 inches.
To find the height of the pyramid, we need to first find the length of "r" using the given information.
From the illustration, we can see that the slant height "s" is labeled and given as 24 in.
Now, we can use the Pythagorean Theorem in the right triangle formed by the slant height "s", the lateral edge length "e", and the height "r".
The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse equals the sum of the squares of the lengths of the other two sides.
In this case, we have:
s^2 = e^2 + r^2
Plugging in the values we know, we have:
24^2 = 25^2 + r^2
Simplifying the equation, we get:
576 = 625 + r^2
Rearranging the equation, we have:
r^2 = 576 - 625
r^2 = -49
Since we're dealing with lengths, the length cannot be negative, so we can disregard this solution.
Therefore, there is no real value for "r", and we cannot proceed to find the height "h" of the pyramid.
Without further information, we cannot answer the question.