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48 A right square pyramid is shown. The height is 10 centimeters and the side length of the base is 16 centimeters. What is the length, in centimeters (cm), of s ? s= cm

4848\newlineA right square pyramid is shown.\newlineThe height is 1010 centimeters and the side length of the base is 1616 centimeters.\newlineWhat is the length, in centimeters (cm) (\mathrm{cm}) , of s s ?\newlines= s= \newlinecm \mathrm{cm}

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Q. 4848\newlineA right square pyramid is shown.\newlineThe height is 1010 centimeters and the side length of the base is 1616 centimeters.\newlineWhat is the length, in centimeters (cm) (\mathrm{cm}) , of s s ?\newlines= s= \newlinecm \mathrm{cm}
  1. Calculate Half Base: To find the slant height ss, we need to use the Pythagorean theorem on the triangle formed by the height of the pyramid, half the base, and the slant height.
  2. Apply Pythagorean Theorem: First, calculate half the base of the square, which is half of 16 cm16\,\text{cm}. Half of base = 16 cm/2=8 cm16\,\text{cm} / 2 = 8\,\text{cm}.
  3. Calculate Squares: Now, apply the Pythagorean theorem: s2=height2+(half of base)2s^2 = \text{height}^2 + (\text{half of base})^2.\newlines2=102+82s^2 = 10^2 + 8^2.
  4. Find Square Root: Calculate the squares: s2=100+64s^2 = 100 + 64.\newlines2=164s^2 = 164.
  5. Calculate Slant Height: Find the square root of 164164 to get the slant height.s=164s = \sqrt{164}.
  6. Calculate Slant Height: Find the square root of 164164 to get the slant height.\newlines=164s = \sqrt{164}.Calculate the square root: s≈12.806s \approx 12.806 cm.

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