Question

what is the area of triangle dfg? round to the nearest whole square unit. herons formula: area = \\( \sqrt { s ( s - a ) ( s - b ) ( s - c ) } \\)

Explanation:

Step1: Calculate the semi - perimeter \(s\)

The formula for the semi - perimeter of a triangle with side lengths \(a\), \(b\), and \(c\) is \(s=\frac{a + b + c}{2}\). Here, \(a = 11\), \(b=6\), \(c = 9\). So, \(s=\frac{11 + 6+9}{2}=\frac{26}{2}=13\).

Step2: Apply Heron's formula

Heron's formula is \(A=\sqrt{s(s - a)(s - b)(s - c)}\). Substitute \(s = 13\), \(a = 11\), \(b = 6\), \(c = 9\) into the formula:

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Answer:

27 square units