Question

find the area of the triangle whose sides are 13 cm 9 cm 6cm

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.

Solution:
Let the sides of the triangle are a=13 m, b=9 m & c= 6 m.
Semi Perimeter of the ∆,s = (a+b+c) /2 s=(13 + 9 + 6) / 2 s= 28/2= 14 m

Using heron’s formula,
Area of the ∆ = √s (s-a) (s-b) (s-c)
= √14(14 - 13) (14 - 9) (14 - 6)
= √14 × 1 × 5 × 8
=√2 ×7 × 5 ×2×2×2
= √(2×2) ×(2×2) × 7 × 5
= 2 × 2 √ 35
=4√35
= 4 × 5.92      [√35 = 5.92]
= 23.68 cm²

Hence, the area of the triangle is 23.68 cm².

HOPE THIS WILL HELP YOU….

Answer 2

Solution :-

Given - 

Three sides of the triangle are 13 cm, 9 cm and 6 cm

Let a = 13 cm, b = 9 cm and c = 6 cm

Area of the triangle = √s(s - 1)(s - b)(s - b)

Semi Perimeter 's' = (a + b + c)/2

⇒ s = (13 + 9 + 6)/2

⇒ 28/2

s = 14 cm

Area = √14(14 - 13)(14 - 9)(14 - 6)

⇒ √14*1*5*8

⇒ √560

⇒ 23.66 sq cm

So, area of the triangle is 23.66 sq cm.

Answer.