A circus tent is in the shape of a square pyramid. Each edge of the square base is 20 m and its slant height is 13.5 m. Find the height of the tent. Round the answer to the nearest tenth.(1 point)

Question

Responses

24.1 cm
24.1 cm
9.1 m 
9.1 m 
14.8 cm
14.8 cm
16.8 m 

Answer 1

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

1. The base of the pyramid is a square with each edge measuring 20 m, so the length of half of one edge (the base's half-diagonal) is: $$\frac{20}{2}=10,\text{m}$$

2. The slant height of the pyramid is given as 13.5 m. The height (h) of the pyramid, the slant height (l), and half of the base edge (10 m) forms a right triangle. According to the Pythagorean theorem: $$l^2=h^2+(10{)}^2$$ Plugging in the values, we have: $$(13.5{)}^2=h^2+{10}^2$$ $$182.25=h^2+100$$

3. Rearranging the equation to solve for $h^2$: $$h^2=182.25-100$$ $$h^2=82.25$$

4. Taking the square root of both sides to find $h$: $$h=\sqrt{82.25}\approx 9.1,\text{m}$$

Therefore, the height of the tent is approximately $9.1,\text{m}$.

The final answer is: 9.1 m