If for an isosceles triangle the length of each equal side

Home » Aptitude » Mensuration » Question

If for an isosceles triangle the length of each equal side is ‘a’ units and that of the third side is ‘b’ units, then its area will be

AD, is perpendicular on BC.
BD = DC = b/2
AD = √AB² - BD²

= √a² -		b		²
		2

= √a² -	b²
	2

=	√4a² - b²
	2

∴ Area of ∆ABC =	1	× BC × AD
	2

=	1	× b	√4a² - b²
	2		2

=	b	√4a² - b² square units.
	4

a	√4b² - a²
4

a	√2a² - b² square units
2

b	√a² - 2b² square units
2