To find the area of a triangle with given side lengths (8 cm, 6 cm, and 10 cm), we can use Heron's formula instead of the base-height formula since we don't have the height.
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First, we calculate the semi-perimeter \( s \): \[ s = \frac{a + b + c}{2} = \frac{8 + 6 + 10}{2} = \frac{24}{2} = 12 , \text{cm} \]
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Next, we use Heron's formula to calculate the area \( A \): \[ A = \sqrt{s(s-a)(s-b)(s-c)} \] Where \( a = 8 , \text{cm}, b = 6 , \text{cm}, c = 10 , \text{cm} \).
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Substitute the values: \[ A = \sqrt{12(12-8)(12-6)(12-10)} = \sqrt{12(4)(6)(2)} \]
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Calculate: \[ A = \sqrt{12 \times 4 \times 6 \times 2} = \sqrt{576} \] \[ A = 24 , \text{cm}^2 \]
Thus, the area of the triangle is \( A = 24 , \text{cm}^2 \).