Question

a stainless - steel patio heater is shaped like a square pyramid. the length of one side of the base is 12 feet. the slant height is 11 feet. what is the height of the heater? round to the nearest tenth of a foot.
the height of the heater is about \\(\square\\) feet.
(round to the nearest tenth as needed.)

Explanation:

Step1: Find half of the base side

The base is a square with side length 12 feet. Half of the side length is $\frac{12}{2} = 6$ feet.

Step2: Use Pythagorean theorem

Let the height of the pyramid be \( h \), the slant height \( l = 11 \) feet, and half of the base side \( a = 6 \) feet. By the Pythagorean theorem, \( h=\sqrt{l^{2}-a^{2}} \). Substitute the values: \( h=\sqrt{11^{2}-6^{2}}=\sqrt{121 - 36}=\sqrt{85}\approx9.2 \) (rounded to the nearest tenth).

Answer:

\( 9.2 \)