untitled

=
a

ac c a b

a

ac c a b

2

2

2

2 2 2 2 ^2 ^2 ^2

˜

  

= 2

2 2 2 2

4

{( ) }{ ( )}

a

ca b b ca

= 2
4

( )( 2 )( 2 () 2 )

a

abc abc b abc a abc c

= 2
4

2 ( 2 2 () 2 2 () 2 2 )

a

s s b s a s c

= 2
4 ( )( )( )
a

ssa sb sc

? ( )( )( )
2
ss a s b s c
a

AD   

Area of 'ABC = BC˜AD
2

1

= ( )( )( )
2
2

1

ss a s b b c

a

˜a˜   

= s(sa)(sb)(bc)

(4) Equilateral Triangle :
Let the length of each side of the equilateral triangular region ABC be a.

Draw ADABC?
2

a

BD CD

In right angled 'ABD

BD^2 AD^2 AB^2

or,
4

3

2 4

2 2

2

2

AD^2 AB^2 BD^2 a^2 a ̧ a a a

¹

·

̈

©

 §

?
2

3 a

AD

Area of 'ABC = ˜BC˜AD
2

1

=
2

3

2

1 a

˜a˜ or,^2

4

3

a

(5) Isosceles triangle :
Let ABC be an isosceles triangle in which AB AC a
andBC b