Question

using heron formula, find the area of a triangle whose side are
1.8m,8m,8.2m .

Answer 1

Heron's Formula

The following Heron's Formula will be used to find the solution:

$\boxed{\begin{array}{l} \bullet \: \: \rm{s = \dfrac{a + b + c}{2}} \\ \\ \bullet \: \: \rm{\sqrt{s(s - a)(s + b)(s - c)}}\end{array}}$

where, $'s'$ is the semi perimeter and $a, b, c$ are the sides of the triangle.

The given values are;

• a = 1.8m
• b = 8m
• c = 8.2m

Now let's find semi-perimeter $'s'$ first. To find semi-perimeter$'s'$ we use,

$\implies\boxed{\bf{s\:=\:{\dfrac{a\:+\:b\:+\:c}{2}}}}$

By using the formula and substituting the known values, we get:

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

$\implies\sf{s\:=\:{\dfrac{1.8\:+\:8\:+\:8.2}{2}}}$

$\implies\sf{s\:=\:{\dfrac{18}{2}}}$

$\implies\sf{s\:=\:9}$

Now, let's find area of traingle using the formula,

$\implies\boxed{\bf{\sqrt{s\:(s\:-\:a)\:(s\:-\:b)\:(s\:-\:c)}}}$

By substituting the known values in the formula, we get:

$\implies\sf\sqrt{9\:(9\:-\:1.8)\:(9\:-\:8)\:(9\:-\:8.2)}$

$\implies\sf\sqrt{9\:(7.2)\:(1)\:(0.8)}$ $\implies\sf\sqrt{9\:(5.76)}$

$\implies\sf\sqrt{9\:\times\:5.76}$

$\implies\sf\sqrt{51.84}$

$\implies\sf{7.2}$

Therefore, the area of the triangle is 7.2m².