To find the area of a triangle using the base (\( b \)) and height (\( h \)), you need the measurements of one side as the base and the corresponding height. However, from the dimensions you've provided (11 cm, 8 cm, and 9 cm), I'm assuming these are the lengths of the sides of the triangle.
When the height is not directly given, we can use Heron's formula to find the area of the triangle. Here’s how you can do it:
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Calculate the semi-perimeter (s) of the triangle using the formula: \[ s = \frac{a + b + c}{2} \] 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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Apply Heron's formula to find the area (A): \[ A = \sqrt{s(s-a)(s-b)(s-c)} \] Substituting the values: \[ A = \sqrt{14(14-11)(14-8)(14-9)} \] \[ A = \sqrt{14 \times 3 \times 6 \times 5} \] \[ A = \sqrt{14 \times 90} = \sqrt{1260} \]
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Calculate \( \sqrt{1260} \) to find the area: \[ 1260 = 36 \times 35 \] hence \[ \sqrt{1260} = \sqrt{36 \times 35} = 6 \sqrt{35} \approx 6 \times 5.916 = 35.496 \text{ cm}^2 \]
Thus, the area of the triangle is approximately: \[ A \approx 35.5 \text{ cm}^2 \]
So the answer is: \[ A \approx 35.5 \text{ cm}^2 \]