Let in 'ABCthe sides are :
BC a,CA b,AB c.
AD is drawn perpendicular from A to BC.
Let altitude (height) AD h.

Considering the angle C, we get, C
CA

AD

sin

or, C
b

h

sin or, h bsinC

Area of 'ABC = BCuAD
2

1

= a bsinC

2

1

u

= absinC

2

1

Similarly, area of 'ABC = bcsinA
2

1

= casinB

2

1

(3) Three sides of a triangle are given.
Let in 'ABC,BC a,CA b and AB c.
? Perimeter of the triangle 2 s abc
We draw ADABC
Let, BD x, so CD ax
In right angled 'ABD and 'ACD
?AD^2 AB^2 BD^2 and AD^2 AC^2 CD^2
?AB^2 BD^2 AC^2 CD^2
or,c^2 x^2 b^2 (ax)^2
or,c^2 x^2 b^2 a^2  2 axx^2
or, 2 ax c^2 a^2 b^2

?
a

c a b

x

2

(^2)  (^2)  2
Again,AD^2 c^2 x^2

2 2 2 2
2
2 ̧
̧
¹
·
̈
̈
©
§  

a
c a b
c
= ̧ ̧
¹
·
̈ ̈
©
§  
̧ ̧ 
¹
·
̈ ̈
©
§  

a
c a b
c
a
c a b
c
2 2
2 2 2 2 2 2