Question

what is the area of triangle dfg? round to the nearest whole square unit. 27 square units 38 square units 364 square units 728 square units heron’s formula: area = \sqrt{s(s - a)(s - b)(s - c)}

Explanation:

Step1: Calculate the semi - perimeter (s)

The sides of the triangle are \(a = 6\), \(b = 9\), \(c = 11\). The formula for the semi - perimeter \(s=\frac{a + b + c}{2}\).
Substitute the values: \(s=\frac{6 + 9+11}{2}=\frac{26}{2}=13\).

Step2: Apply Heron's formula

Heron's formula for the area of a triangle is \(A=\sqrt{s(s - a)(s - b)(s - c)}\).
Substitute \(s = 13\), \(a = 6\), \(b = 9\), \(c = 11\) into the formula:
\(A=\sqrt{13(13 - 6)(13 - 9)(13 - 11)}\)
First, calculate the values inside the square root:
\(13-6 = 7\), \(13 - 9=4\), \(13 - 11 = 2\)
Then, \(A=\sqrt{13\times7\times4\times2}=\sqrt{13\times7\times8}=\sqrt{728}\approx26.98\approx27\)

Answer:

27 square units