What is the height of the paperweight if the length of the square base is 4 in. and the slant height is 3 in.?

To find the height of the square pyramid (paperweight), we can use the Pythagorean theorem.

1. The slant height (l) is the hypotenuse of a right triangle formed by half the base length (b) and the height (h).
2. Here, the base length is 4 in., so half the base (b/2) is 2 in.
3. We know the slant height (l) is 3 in.

Using the Pythagorean theorem:

[ l^2 = (b/2)^2 + h^2 ]

Substituting the values:

[ 3^2 = 2^2 + h^2 ]

[ 9 = 4 + h^2 ]

[ h^2 = 9 – 4 ]

[ h^2 = 5 ]

[ h = sqrt{5} approx 2.2 text{ in.} ]

So, the height of the paperweight rounded to the nearest tenth of an inch is approximately 2.2 in.