Question

How is the formula of .....is formed
Please explain it briefly

Answer 1

Heya dear !!!



Let ∆ABC has three different sides.



AB not Equal BC not equal AC.




We can find the area of ∆ABC by using herons formula.


Which is,



✓ S ( S - A ) ( S - B) ( S -C)



Where,


S = Semi Perimeter


And ,


Formula for finding the semi Perimeter of ∆ABC is



Semi Perimeter ( S) = 1/2 × ( A + B + C)



Where,


A , B and C are the three different sides of triangle ABC.



Let see an example,



Question :- AB = 10 cm , AC = 20 cm and BC = 30 cm of ∆ABC . Find the area of triangle ABC.



As we can see that,



The sidea of triangle ABC is different from each other.

So,


We will have to use herons formula for finding the area of ∆ABC.



AB = 10 cm


AC = 20 cm


And,


BC = 30 cm



Therefore,


Semi Perimeter (S) of ∆ABC = 1/2 × ( AB + AC + BC)



=> 1/2 × ( 10 + 20 + 30)



=> 1/2 × ( 60)


=> 30 cm


Therefore,


Area of ∆ABC = ✓ ( S - AB) ( S - AC ) ( S -BC)




=> ✓ 30 ( 30 - 10) ( 30 - 20) ( 30 -30)



=> ✓30 ( 20 ) × (10) × (0)




=> ✓ 6000 cm²


=> 77.45 cm².






HOPE U GOT IT..