To find the area of the triangle with sides of 11 cm, 8 cm, and 9 cm, we first need to use Heron's formula, since the height is not provided directly.
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Calculate the semi-perimeter (s): \[ s = \frac{a + b + c}{2} \] where \(a = 11\) cm, \(b = 8\) cm, and \(c = 9\) cm. \[ s = \frac{11 + 8 + 9}{2} = \frac{28}{2} = 14 \text{ cm} \]
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Use Heron's Formula to calculate the area (A): \[ A = \sqrt{s(s-a)(s-b)(s-c)} \] \[ A = \sqrt{14(14-11)(14-8)(14-9)} \] \[ A = \sqrt{14 \times 3 \times 6 \times 5} \] \[ A = \sqrt{14 \times 90} = \sqrt{1260} \]
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Calculate \(\sqrt{1260}\): To simplify \(\sqrt{1260}\): \[ 1260 = 9 \times 140 = 9 \times 14 \times 10 \] The area \(A\) is calculated as follows: \[ \sqrt{1260} \approx 35.5 \text{ cm}^2 \]
The approximate area of the triangle is: \[ A \approx 35.5 \text{ cm}² \]
Final Answer: \[ A \approx 35.5 \text{ cm}² \]