Three squares have dimensions indicated in the diagram. The area of the quadrilateral ABCD is?
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Given : Three squares have sides 2 , 3 and 5
To Find: The area of the quadrilateral ABCD
Solution:
Larger right angle triangle EGF has
Base = 2 + 3 + 5 = 10
Perpendicular = 5
ΔEGF ~ ΔEAB using AA similarity
as ∠E common and ∠EGF = ∠EAB = 90°
=> AB/GF = EA/EG
=> AB/5 = 2/10
=> AB = 1
Similarly ΔEGF ~ ΔEDC
=> CD/5 = 5 /10
=> CD = 2.5
quadrilateral ABCD is trapezium
area of ABCD = (1/2) (AB + CD) * AD
= (1/2) ( 1 + 2.5 ) * 3
= 10.5/2
= 5.25 sq units
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