# What is the area of a triangle with sides of length 2, 4, and 5?

Aug 4, 2018

Area is $3.8$ square units

#### Explanation:

If three sides of a triangle are $a , b$ and $c$, then

its area is $\sqrt{s \left(s - a\right) \left(s - b\right) \left(s - c\right)}$, where $s = \frac{a + b + c}{2}$

Here sides are $2 , 4$ and $5$ and hence $s = \frac{2 + 4 + 5}{2} = \frac{11}{2}$

and area of triangle is

$\sqrt{\frac{11}{2} \left(\frac{11}{2} - 2\right) \left(\frac{11}{2} - 4\right) \left(\frac{11}{2} - 5\right)}$

= $\sqrt{\frac{11}{2} \times \frac{7}{2} \times \frac{3}{2} \times \frac{1}{2}}$

= $\frac{1}{4} \sqrt{231} = \frac{15.19868}{4} = 3.79967$ or say $3.8$