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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

Analyze the diagram below and complete the instructions that follow. Find the area-example-1

1 Answer

5 votes
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
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