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The area KK of a triangle with sidesaa, bb, and cc is K=K=\text{_______} where S = \text{_______}.

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Full solution

Q. The area KK of a triangle with sidesaa, bb, and cc is K=K=\text{_______} where S = \text{_______}.
  1. Identify Formula: Identify the formula to use for the area of a triangle when the sides are known.\newlineWe use Heron's formula, which states that the area K of a triangle with sides a, b, and c is given by K=s(s−a)(s−b)(s−c) K = \sqrt{s(s-a)(s-b)(s-c)} where s s is the semi-perimeter of the triangle.
  2. Calculate Semi-Perimeter: Calculate the semi-perimeter s.\newlineThe semi-perimeter s s is calculated as s=a+b+c2 s = \frac{a+b+c}{2} .
  3. Substitute Value: Substitute the value of s back into Heron's formula.\newlineUsing s s from the previous step, substitute into the area formula: K=s(s−a)(s−b)(s−c) K = \sqrt{s(s-a)(s-b)(s-c)} .

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