A ceramic paperweight is shaped like a square pyramid. The length of the square base and the slant height is shown. What is the height of the paperweight? Round to the nearest tenth of an inch.
A square pyramid with base edge of length 3 inches and slant height of length 4 inches.
To find the height of the paperweight, we can use the Pythagorean theorem.
The height (h) of the paperweight is the unknown we are looking for. We know the base edge length (b) is 3 inches and the slant height (s) is 4 inches.
Using the Pythagorean theorem, we have:
(3/2)^2 + h^2 = 4^2
9/4 + h^2 = 16
h^2 = 16 - 9/4
h^2 = 64/4 - 9/4
h^2 = 55/4
h = sqrt(55/4)
h ≈ 3.7 inches
Therefore, the height of the ceramic paperweight is approximately 3.7 inches.