Question

a stainless - steel patio heater is shaped like a square pyramid. the length of one side of the base is 6 feet. the slant height is 10 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 base half-length

The base is a square with side 6 ft, so half the side length is $\frac{6}{2}=3$ feet.

Step2: Use Pythagorean theorem

The slant height, height of the pyramid, and half the base side form a right triangle. Let $h$ = height of the heater.
$$h = \sqrt{10^2 - 3^2}$$

Step3: Calculate the value

$$h = \sqrt{100 - 9} = \sqrt{91} \approx 9.539$$

Step4: Round to nearest tenth

Round $\sqrt{91}$ to one decimal place.

Answer:

9.5