Question

The sides of a triangle are 3 cm, 5 cm and 6 cm. What is its area?FIND USING HERON 'S FORMULA​

Answer 1

Given :-

• First side of triangle (a) = 3 cm

• Second side of triangle (b) = 5 cm

• Third side of triangle (c) = 6cm

To find :-

• Area of triangle

Solution :-

$\rm\:s=\dfrac{a+b+c}{2}$

$\rm\longrightarrow\:s=\dfrac{3+5+6}{2}$

$\rm\longrightarrow\:s=\cancel\dfrac{14}{2}$

$\rm\longrightarrow\:s=7\:cm$

By using Heron's formula,

we know that,

$\small\orange{\bigstar}\:\:{\underline{\boxed{\bf\pink{Area=\sqrt{s(s-a)(s-b)(s-c)}}}}}$

$\rm\longrightarrow\:\sqrt{7(7-3)(7-5)(7-6)}$

$\rm\longrightarrow\sqrt{7\times\:4\times\:2\times\:1}$

$\rm\longrightarrow\:\sqrt{7\times\:2\times\:2\times\:2\times\:1}$

$\rm\longrightarrow\:2\sqrt{14}$

$\rm\longrightarrow\:2\times\:3.74$

$\rm\longrightarrow\:7.48\:c{m}^{2}$

Hence,the area of triangle will be 7.48 cm².