A = \frac{1}{2} \times 9 \times 12 = 54
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- Thus, the length of each side of the hexagon is \(\boxed{6}\).
- Question: A circle is inscribed in a right triangle with legs of lengths \(9\) units and \(12\) units. Find the radius of the inscribed circle.
- Solution: The area \(A\) of the triangle is given by:
- s = \frac{9 + 12 + 15}{2} = 18
- where \(15\) is the hypotenuse, calculated by \(c = \sqrt{9^2 + 12^2} = 15\). The radius \(r\) of the inscribed circle is given by:
- r = \frac{A}{s} = \frac{54}{18} = 3
