Question

"Question 6 An isosceles triangle has perimeter 30 cm and each of the equal sides is 12 cm. Find the area of the triangle.

Class 9 - Math - Heron's Formula Page 203"

Answer 1

The perimeter of a triangle is equal to the sum of its three sides it is denoted by 2S.

2s=(a+b+c)

s=(a+b+c)/2

Here ,s is called semi perimeter of a triangle.

 

The formula given by Heron about the area of a triangle is known as Heron's formula. According to this formula area of a triangle= √s (s-a) (s-b) (s-c)

Where a, b and c are three sides of a triangle and s is a semi perimeter.

 

This formula can be used for any triangle to calculate its area and it is very useful when it is not possible to find the height of the triangle easily . Heron's formula is  generally used for calculating area of scalene triangle.

____________________________________________________________

Given ,perimeter of a isosceles triangle=30cm

Let the given sides be a= 12cm, b= 12 cm

& Let c= x cm

Perimeter of a triangle=a+b+c

30= 12+12+x

30= 24+x

X=30-24=6

Third side(c)= 6 cm

 semi perimeter of a triangle(s)= perimeter of a triangle/2

s= 30/2= 15

s=15 cm

Using heron’s formula,
Area of the triangle = √s (s-a) (s-b) (s-c)

= √15(15 – 12) (15 – 12) (15 – 6)

= √15 × 3 × 3 × 9

= √ 3×5×3×3×3×3

=3×3√15

=9√15 cm²

Hence, the area of an  isosceles triangle is= 9√15 cm²

=========================================================

Hope this will help you....