Question

Using heron's formula, find the area of triangle whose sides are 10cm,24cm,26cm

Answer 1

120 cm ^2 is the correct answer

Answer 2

${\large{\text{\underline{\underline{\red{Given :}}}}}}$

$\text{Sides of triangle : 10cm, 24cm, 26cm}$

${\large{\text{\underline{\underline{\red{To Find :}}}}}}$

$\text{Area of triangle}$

${\large{\text{\underline{\underline{\red{Formula Applied :}}}}}}$

$\text{Heron's formula}$

${\large{\text{\underline{\underline{\red{Solution :}}}}}}$

Let a =10 cm, b = 24cm, c = 26cm

${\text{heron's formula} = \sqrt{s(s-a)(s-b)(s-c)}}$

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

$s=\frac{10+24+26}{2} \implies \frac{60cm}{2} \implies 30cm$

$\sf s-a\implies 30-10\implies 20 cm$

$\sf s-b\implies 30-24\implies 6cm$

$\sf s-c\implies 30-26\implies4cm$

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

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

$\implies \sqrt{2\times3\times5\times2^2\times5\times2\times3\times2^2}$

$\implies \sqrt{2^6\times3^2 \times5^2}$

$\implies 2^3\times3\times5$

$\implies 8\times3\times 5$

$\implies 120cm^2$

$\text{Area of triangle is 120 cm^2 }$

________________________________________

${\large{\text{\underline{\underline{\red{Heron's formula :}}}}}}$

Heron a mathematician gave a formula for finding the area of a triangle, if the height is not known, but the length of the three sides are known. If        a, b, c denotes the sides of BC,AC and AB respectively of a triangle ABC, then

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

where $s = \frac{a+b+c}{2}$

( NOTE : When $a=b=c,$ then Heron's formula will be $\frac{\sqrt{3}}{4}a^2sq.units$ which is area of an equailateral triangle. )