Use 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
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(1 point)
The height of the square pyramid is
___ in.
step-by-step bot
To find the height of the pyramid, we can use the Pythagorean theorem. Let's label the right triangle formed by the height line, the slant height line, and the line segment connecting the center of the base to the center of the right base edge as triangle OHR.
Using the Pythagorean theorem, we have:
r² + h² = s²
Since we already know that s is 24 inches and e is 25 inches, we can find r.
r = √(e² - s²)
r = √(25² - 24²)
r = √(625 - 576)
r = √49
r = 7 inches
Now that we know r, we can substitute the values into the Pythagorean theorem to find h:
7² + h² = 24²
49 + h² = 576
h² = 576 - 49
h² = 527
h ≈ √527
h ≈ 22.92
Rounding to the nearest whole number, the height of the square pyramid is 23 inches.