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

Mar 26, 2018

color(blue)("Area of the triangle " A_t = 3.8 " sq units"

#### Explanation:

$\text{Given : } a = 2 , b = 4 , c = 5$

Having known three sides, we can calculate the area of the triangle using the formula,

${A}_{t} = \sqrt{s \cdot \left(s - a\right) \cdot \left(s - b\right) \cdot \left(s - c\right)}$

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

$s = \frac{a + b + c}{2} = \frac{2 + 4 + 5}{2} = 5.5$

${A}_{t} = \sqrt{5.5 \cdot \left(5.5 - 2\right) \cdot \left(5.5 - 4\right) \cdot \left(5.5 - 5\right)}$

$\implies \sqrt{5.5 \cdot 3.5 \cdot 1.5 \cdot 0.5} \approx 3.8 \text{ sq units}$