To find the height of the square pyramid (the circus tent), we can use the Pythagorean theorem.
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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: \[ \frac{20}{2} = 10 , \text{m} \]
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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: \[ (13.5)^2 = h^2 + 10^2 \] \[ 182.25 = h^2 + 100 \]
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Rearranging the equation to solve for \(h^2\): \[ h^2 = 182.25 - 100 \] \[ h^2 = 82.25 \]
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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