Question

The sides of a triangle are $150\mathrm{cm},100\mathrm{cm}\mathrm{and}200\mathrm{cm}$. find the area of the triangle.

Answer 1

The sides of a triangle are $150\mathrm{cm},100\mathrm{cm}\mathrm{and}200\mathrm{cm}$ respectively.

If three sides are given, then the area of a triangle can be calculated using Heron’s formula:

Thus, the area of a triangle using Heron’s formula$=\sqrt{\mathrm{s}(\mathrm{s}-\mathrm{a})(\mathrm{s}-\mathrm{b})(\mathrm{s}-\mathrm{c})}\mathrm{square}\mathrm{units}.$

Where,$\mathrm{a}=150\mathrm{cm},\mathrm{b}=100\mathrm{cm}\mathrm{and}\mathrm{c}=200\mathrm{cm}$

$“\mathrm{s}”\mathrm{is}\mathrm{the}\mathrm{semi}-\mathrm{perimeter}=\frac{(\mathrm{a}+\mathrm{b}+\mathrm{c})}{2}=\frac{(150+100+200)}{2}=\frac{450}{2}=225$

Now, substitute the values in the area formula, we get

$\mathrm{A}=\sqrt{\left[225\right(225-150\left)\right(225-100\left)\right(225-200\left)\right]}$

On simplifying the above expression, we get

$\mathrm{A}=1875\sqrt{15}$

In decimal form,$\mathrm{A}=7261.8437$

Therefore, the area of a triangle is $7261.8437{\mathrm{cm}}^2$