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 semi - perimeter

Let \(a = 11\), \(b = 6\), \(c = 9\). The semi - perimeter \(s=\frac{a + b + c}{2}=\frac{11+6 + 9}{2}=\frac{26}{2}=13\).

Step2: Apply Heron's formula

The area \(A=\sqrt{s(s - a)(s - b)(s - c)}=\sqrt{13(13 - 11)(13 - 6)(13 - 9)}=\sqrt{13\times2\times7\times4}=\sqrt{728}\approx27\).

Answer:

27 square units