In triangle EFG,
EG = 4.8 units
Since angle FDE = angle FED,
EF = FD = 3.5 units [sides opposite to equal angles]
FG = DE = 3 units [Given]
s = (a+b+c)/2
= (EG+EF+GF)/2
= (4.8+3.5+3)/2
= 11.3/2
now using Heron's formula,
area of EFG =
[tex] \sqrt{s(s - a)(s - b)(s - c)} \\ = \sqrt{ \frac{11.3}{2}(\frac{11.3}{2} - 4.8)( \frac{11.3}{2} - 3.5)( \frac{11.3}{2} - 3)} \\ = \sqrt{ \frac{11.3}{2} (5.65 - 4.8)(5.65 - 3.5)(5.65 - 3) } \\ = \sqrt{ 5.65\times 0.85 \times 2.15 \times 2.65} \\ = \sqrt{27.36224375} \\ = 5.23089\\ = 5.2 \: units^2[/tex]
