Answer: 9.8 cm
Explanation:
To find the slant height of a 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 the diagonal of the base.
Given: Base area = 64 cm² Height = 8 cm
1. Find the length of the diagonal of the base: Since the base is squared, it has four equal sides. Let's call the length of each side of the base "s".
The area of a square is given by side^2, so we can set up the equation: s^2 = 64 Taking the square root of both sides gives us: s = √64 s = 8 cm
2. Find half the diagonal of the base: The diagonal of a square can be found using the Pythagorean theorem. Let's call half the diagonal "d".
Using the length of each side of the base (s), we can set up the equation: d^2 = (s/2)^2 + (s/2)^2 d^2 = (8/2)^2 + (8/2)^2 d^2 = 4^2 + 4^2 d^2 = 16 + 16 d^2 = 32
Taking the square root of both sides gives us: d = √32 d ≈ 5.66 cm
3. Find the slant height: The slant height is the hypotenuse of a right triangle formed by the height of the pyramid (8 cm) and half the diagonal of the base (5.66 cm).
Using the Pythagorean theorem, we can set up the equation: slant height^2 = height^2 + (half diagonal)^2 slant height^2 = 8^2 + 5.66^2 slant height^2 = 64 + 32 slant height^2 = 96
Taking the square root of both sides gives us: slant height ≈ √96 slant height ≈ 9.8 cm
So, the slant height of the pyramid is approximately 9.8 cm.