In ∆ABC, D and E are two points on the sides AB and

Home » Aptitude » Mensuration » Question

DE || BC
∴ ∠ADE = ∠ABC
∠AED = ∠ACB
∴ ∆ADE ~ ∆ABC

∴	AD	=	2
	BD		3

⇒	BD	=	3
	AD		2

=	BD	+ 1 =	3	+ 1
	AD		2

⇒	BD + AD
	AD

⇒	3 + 2	⇒	AB	=	5
	2		AD		2

∴	Area of ∆ADE	=	AD²	=		2		²	=	4
	Area of ∆ABC		AB²			5		25

⇒ 1 -	Area of ∆ADE	= 1 -	4
	Area of ∆ABC		25

⇒	Area of ∆ABC - Area of ∆ADE	=	25 - 4
	Area of ∆ABC		25

∴	Area of trapezium DECB	=	21
	Area of ∆ABC		25