Area of a Triangle – by Heron’s Formula

The formula of area of a triangle is given by heron and it is also called Hero’s Formula.

Area of triangle \mathrm{=\sqrt{s(s-a)(s-b)(s-c)}}

where a, b and c are the sides of the triangle and s is the semiperimeter 

\mathrm{s=\dfrac{a+b+c}{2}}

Generally, this formula is used when the height of the triangle is not possible to find or you can say if the triangle is a scalene triangle.

Here the sides of triangle are

AB = 12 cm

BC = 14 cm

AC = 6 cm

\text s=\dfrac{14+12+6}{2}=\dfrac{32}{2}=16\ \text{cm}

Area of triangle \mathrm{=\sqrt{16(16-12)(16-14)(16-6)}}

=\sqrt{16(4)(2)(10)}=\sqrt{1280}=35.77\ \text{cm}^2 .

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