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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