To find the height of the square pyramid tent, we can use the Pythagorean theorem in three dimensions, considering the right triangle formed by the height of the tent, half the length of the base, and the slant height.
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The length of each edge of the square base is 20 meters, so half the length of the base is: \[ \frac{20}{2} = 10 \text{ meters} \]
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The slant height (l) is given as 13.5 meters.
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We can denote the height (h) of the pyramid. According to the Pythagorean theorem: \[ l^2 = h^2 + \left(\frac{b}{2}\right)^2 \] where \( b \) is the length of a side of the base.
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Plugging in the values: \[ (13.5)^2 = h^2 + (10)^2 \] \[ 182.25 = h^2 + 100 \] \[ h^2 = 182.25 - 100 \] \[ h^2 = 82.25 \] \[ h = \sqrt{82.25} \approx 9.1 \text{ meters} \]
Therefore, the height of the tent, rounded to the nearest tenth, is 9.1 m.