To find the area of a triangle with sides measuring 8 cm, 9 cm, and 11 cm, we can use Heron's formula rather than the base-height formula, as we don't have the height of the triangle.
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Calculate the semi-perimeter (s) of the triangle: \[ s = \frac{a + b + c}{2} = \frac{8 + 9 + 11}{2} = \frac{28}{2} = 14 \text{ cm} \]
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Apply Heron's formula to find the area (A): \[ A = \sqrt{s(s-a)(s-b)(s-c)} \] where \( a = 8 \) cm, \( b = 9 \) cm, and \( c = 11 \) cm.
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Plug in the values: \[ A = \sqrt{14(14-8)(14-9)(14-11)} \] Simplifying inside the parentheses: \[ = \sqrt{14 \times 6 \times 5 \times 3} \]
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Calculate each step:
- First calculate \( 14 \times 6 = 84 \)
- Then calculate \( 84 \times 5 = 420 \)
- Finally, calculate \( 420 \times 3 = 1260 \)
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Find the square root: \[ A = \sqrt{1260} \] Approximating the square root: \[ \sqrt{1260} \approx 35.5 \text{ cm}^2 \]
Thus, the area of the triangle is approximately: \[ A \approx 35.5 \text{ cm}^2 \]