Area with Herons Formula


 
 
Concept Explanation
 

Area with Herons Formula

Heron's Formula : In some cases, length of each side of the triangle are given but height of the triangle is neither given nor we are able to find in any way, then to find the area of such type of triangle, we use Heron's formula which is given below.

Area of triangle = large sqrt{s(s-a)(s-b)(s-c)},  where a,b,c are length of the sides of a triangle and s is the semi-perimeter of the triangle i.e. large s=frac{a+b+c}{2}

Example:  Find the area of a quadrilateral ABCD in which AB = 3 cm, BC = 4 cm, CD = 4 cm, DA = 5 cm and AC = 5 cm.

Solution :  We divide the quadrilateral  ABCD in two triangle ABC and ACD

For large Delta ABC, a = 3, b = 4, c = 5 and large s= frac{3+4+5}{2}=6

Area (large DeltaABC) = large sqrt{s(s-a)(s-b)(s-c)}

                                               =  large sqrt{6(6-3)(6-4)(6-5)}=sqrt{6times 3times 2times 1= 6 large ^{cm^{2}}

Similarly, for large Delta ACD,

a = 5 cm, b = 5 cm, c = 4 cm and s =large frac{5+5+4}{2}=7

Area (large Delta ACD ) = large {sqrt{s(s -a)(s - b)(s - c)} =large {sqrt{7(7 -5)(7- 5)(7- 4)}

  =large sqrt{7times 2times 2times 3}   =  large 2sqrt{21}cm^{2}

large therefore Area of quadrilateral ABCD = Area of triangle ABC+ Area of triangle ACD = large 6cm^{2} + large 2sqrt{21}cm^{2}

 

Sample Questions
(More Questions for each concept available in Login)
Question : 1

A triangular park ABC has sides 120 m,80m and 50 m.A gardener has to put a fence all around it and also plant grass inside.Find the area of garden and cost of fencing the garden with barbed wire at the rate of Rs 20 per metre leaving a space 3 m wide for a gate on one side are

Right Option : A
View Explanation
Explanation
Question : 2

If the sides of a triangle are doubled, then its area ______________.

Right Option : D
View Explanation
Explanation
Question : 3

If every side of a triangle is doubled, then increase in the area of the triangle is _________________

Right Option : A
View Explanation
Explanation
 
Video Link - Have a look !!!
 
Language - English
 
 
 
Related Videos
Language - English
Language - English
Language - English

Language - English


Students / Parents Reviews [10]