Find the area of the equilateral triangle given below:
Given: AD=10 cm.
1003√3 cm2
Let us assume AB=BC =AC =2a cm
Then BD =DC = a cm
In ΔABD,
AD2+BD2=AB2
102+a2=(2a)2 [Since AD = 10 cm]
⇒4a2−a2=100
⇒3a2=100
⇒a2=1003−−−(1)
Area of equilateral triangle =√34(side)2
=√34(2a)2
=√34.4a2
=√3a2
=√3.1003 [From (1)]
=1003√3 cm2
Alternate Solution:
Area of equilateral triangle with height ′h′=h2√3
∴ Area =102√3=100√3=1003√3 cm2