Question

define heron's formula??with example

Answer 1

hey there !!

let a , b , c be the side of ∆ ABC and s be the semiperimeter

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

now heron's FORMULA say that.


Area = √s(s-a)(s-b)(s-c)

______________________________

hope it will help you

Answer 2

bonjour!

Heron's formula is named after Hero of Alexendria, a Greek Engineer and Mathematician in 10 - 70 AD. You can use this formula to find the area of a triangle using the 3 side lengths.

Therefore, you do not have to rely on the formula for area that uses base and height. The picture below illustrates the general fromula  where S represents the semi-perimeter of the triangle

-------------------------- HERONS FORMULA--------------------------

$S=\frac{a+b+c}{2}$

where s is called semiperimeter

$Area =\sqrt{s(s-a)(s-b)(s-c)}$

Straight forward example)

Use Heron's formula to find the area of triangle ABC, if side AB = 3 , BC = 2, CA =4

Step 1

Calculate the semi perimeter, S

S = (3+2+4) /2  

S = 9/2 = 4.5

Step 2

Substitute S into the formula

$A =\sqrt{4.5(4.5-2)(4.5-3)(4.5-4)$    

$\sqrt{4.5(2.5)(1.5)(0.5)}$

$\sqrt{8.4375} = 2.9$

Round answer to nearest tenth

Since Heron's formula relates the side lengths, perimeter and area of a triangle, you might need to answer questions the like the following example.

hope it helps

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