Question

find the area of triangles who side are 12 and 16 and perimeter is 36 by herons formuls

Answer 1

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GIVEN :-

a = 12cn

b = 16cm

c = ?

TO FIND :-

Area of the Triangle by Herons Formula.

SOLUTION :-

Perimeter = a + b + c

36 = 12 + 16 + c

36 = 28 + c

36 - 28 = c

C = 8

Now semi perimeter, 

S = a + b + c/2

= 12 + 16 + 8 / 2

= 32 Cm.

Using heron's formula,

Area of triangle

= √s( s − a )( s − b )( s − c )

=√32( 32 − 12 )( 32 − 16 )( 32 − 8 )

= 32 × 20 × 16 × 24

= 16 × 2 × 2 × 5 × 2 × 16 × 12 × 2

= 16 × 2 × 2 √5 × 12

= 16 × 2√60

= 32√60

= 247 Cm².

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