# USE HERONS FORMULA TO FIND THE AREA OF THE TRIANGLE

## About "Use Herons Formula to Find the Area of the Triangle"

Use Herons Formula to Find the Area of the Triangle :

Here we are going to see some example problems to find the area triangle using herons formula.

If a, b and c are the sides of a triangle, then

the area of a triangle = s(s − a)(s − b)(s − c) sq.units.

where s = (a + b + c)/2

‘s’ is the semi-perimeter (that is half of the perimeter) of the triangle.

## Use Herons Formula to Find the Area of the Triangle - Practice questions

Question 1 :

Using Heron’s formula, find the area of a triangle whose sides are

(i) 10 cm, 24 cm, 26 cm

Solution :

a = 10 cm, b = 24 cm and c = 26 cm

s  = (a + b + c)/2

s  =  (10 + 24 + 26)/2

s  =  60/2  =  30

s - a  =  30 - 10  =  20

s - b  =  30 - 24  =  6

s - c  =  30 - 26  =  4

s(s − a)(s − b)(s − c)   =   √30(20)(6)(4)

=  120 cm2

(ii) 1.8 m, 8 m, 8.2 m

Solution :

a = 1.8 m, b = 8 m and c = 8.2 m

s  = (a + b + c)/2

s  =  (1.8 + 8 + 8.2)/2

s  =  18/2  =  9

s - a  =  9 - 1.8  =  7.2

s - b  =  9 - 8  =  1

s - c  =  9 - 8.2  =  0.8

s(s − a)(s − b)(s − c)   =   √9(7.2)(1)(0.8)

=  7.2 m2

Question 2 :

The sides of the triangular ground are 22 m, 120 m and 122 m. Find the area and cost of levelling the ground at the rate of ₹ 20 per m2.

Solution :

a = 22 m, b = 120 m and c = 122 m

s  = (a + b + c)/2

s  =  (22 + 120 + 122)/2

s  =  264/2  =  132

s - a  =  132 - 22  = 110

s - b  =  132 - 120  =  12

s - c  =  132 - 122  =  10

s(s − a)(s − b)(s − c)   =   √132(110)(12)(10)

=   √(11 ⋅ 12 ⋅ 11 ⋅ 10 ⋅ 12 ⋅ 10)

=  11 ⋅ 12 ⋅ 10

=  1320 m2

Cost of leveling the ground  =  ₹ 20 per m2.

Required cost  =  20(1320)

=  ₹ 26400

After having gone through the stuff given above, we hope that the students would have understood, "Use Herons Formula to Find the Area of the Triangle"

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