Question

Analyze the diagram below and complete the instructions that follow. Find the area of EFG.

A.3.4
B. 5.2
C. 68.3
D.68.9

Answer 1

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 =

`√(s(s - a)(s - b)(s - c)) \\ = \sqrt{ (11.3)/(2)((11.3)/(2) - 4.8)( (11.3)/(2) - 3.5)( (11.3)/(2) - 3)} \\ = \sqrt{ (11.3)/(2) (5.65 - 4.8)(5.65 - 3.5)(5.65 - 3) } \\ = √( 5.65* 0.85 * 2.15 * 2.65) \\ = √(27.36224375) \\ = 5.23089\\ = 5.2 \: units^2`