Question

Find the area of a triangle in ${cm}^2$, whose sides are: $10cm,24cm$ and $26cm$

Answer 1

Herons Formula:

Area of triangle with $a,b,c$ as sides and $s=\frac{a+b+c}{2}$

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

where, $a,b,c$ are three sides of the triangles and $s$ is semi-perimeter.

For triangle with sides $10cm$, $24cm$ and $26cm$,

$s=\frac{10+24+26}{2}=30$

Area of the triangle with sides $10cm$, $24cm$ and $26cm$

$=\sqrt{30(30-10)(30-24)(30-26)}$

$=\sqrt{30\times 20\times 6\times 4}$

$=\sqrt{(6\times 5)\times (4\times 5)\times 6\times 4}$

$=\sqrt{(6\times 6)\times (5\times 5)\times (4\times 4)}$

$=6\times 5\times 4$

$=120{cm}^2$