To find the height of the tent, we can use the properties of a square pyramid along with the Pythagorean theorem.
- First, let's denote the height of the pyramid as \( h \).
- The base of the pyramid is a square with each side measuring 20 m, so the distance from the center of the base (the midpoint of the diagonal of the square) to the vertex of the square base will be half the base's length: \[ \text{Half of base edge} = \frac{20 , \text{m}}{2} = 10 , \text{m} \]
- The slant height (the length from the apex of the pyramid down to the midpoint of one of the edges of the base) is given as 13.5 m.
Now, we can apply the Pythagorean theorem in the right triangle formed by the height of the pyramid \( h \), the half base length (10 m), and the slant height (13.5 m): \[ h^2 + (10 , \text{m})^2 = (13.5 , \text{m})^2 \] Expanding this gives: \[ h^2 + 100 = 182.25 \] Now, we can solve for \( h^2 \): \[ h^2 = 182.25 - 100 = 82.25 \] Taking the square root of both sides, we find: \[ h = \sqrt{82.25} \approx 9.1 , \text{m} \]
Rounding this to the nearest tenth, we get \( 9.1 , \text{m} \).
Thus, the height of the tent is: 9.1 cm (as stated in the options, a small correction would be to understand the height of the tent reaches approximately 9.1 meters).
Final answer: 2. 9.1 cm.
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