Question

find the area of a triangle two sidesof which are 18cm 10cm and the perimeter is 42 cm

Answer 1

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Answer 2

Solutions :-.

In a triangle there are three sides.

We have,

Suppose side

a = 18 cm

b = 10 cm

c = ?

Perimeter = 42 cm

Let the third side be c

We know,

Perimeter of triangle = sum of all sides

=> perimeter = a + b + c

=> 42 = 18 + 10 + c

=> c = 42 - 28 = 14

So,

Side c = 14 cm

Find the semi perimeter of triangle :-

Semi perimeter ( S ) = (a + b + c)/2

= (18 + 10 + 14)/2 cm

= 42/2 cm  = 21 cm

Now,

By heron's formula :

Area of triangle =>

= √{s (s - a) (s - b) (s - c)} square unit

= √{21 (21 - 18) (21 - 10) (21 - 14)} cm²

= √{ 21 × 3 × 11 × 7} cm²

= √4851 cm²

= 69.64 cm² approx.

Hence,

Area of triangle is 69.64 cm²