Find the slant height of the square pyramid. 12 cm, 10 cm.
To find the slant height of a square pyramid, we can use the Pythagorean theorem.
The slant height is the hypotenuse of a right triangle formed by the height of the pyramid and half of the diagonal of the square base.
First, let's find the length of the diagonal of the square base. Since it is a square, the diagonal divides the square into two congruent right triangles.
Using the Pythagorean theorem, we can find the length of the diagonal:
d² = a² + a² (where d is the diagonal and a is the side length of the square)
d² = 10² + 10²
d² = 100 + 100
d² = 200
d = √200 ≈ 14.14 cm
Next, let's find the slant height using this diagonal and the height of the pyramid.
Using the Pythagorean theorem again, we can find the slant height:
s² = h² + d² (where s is the slant height and h is the height of the pyramid)
s² = 12² + 14.14²
s² = 144 + 200
s² = 344
s = √344 ≈ 18.55 cm
Therefore, the slant height of the square pyramid is approximately 18.55 cm.
wrong.
I apologize for the mistake.
To find the slant height of a square pyramid, we can use the Pythagorean theorem.
The slant height is the hypotenuse of a right triangle formed by the height of the pyramid and half of the side length of the base.
Let's denote the side length of the square base as "a" and the height of the pyramid as "h".
Using the Pythagorean theorem, the slant height "s" can be found as:
s² = h² + (a/2)²
Given that the height of the pyramid is 12 cm and the side length of the square base is 10 cm, we can calculate the slant height.
s² = 12² + (10/2)²
s² = 144 + 25
s² = 169
s = √169
s = 13 cm
Therefore, the slant height of the square pyramid is 13 cm.