Chapter 8, Problem 41RE

To determine

To find: The area of the triangle.

Answer to Problem 41RE

The value of the area of the triangle is $3.799\text{square}\text{unit}$ .

Explanation of Solution

Given:

The given sides are,

  $\begin{array}{l}a=4\\ b=2\\ c=5\end{array}$

Calculation:

Consider the given sides are,

  $\begin{array}{l}a=4\\ b=2\\ c=5\end{array}$

Consider the Heron’sformula for the area of the triangle is,

  $K=\sqrt{s\left(s-a\right)\left(s-b\right)\left(s-c\right)}$

Consider the expression for $s$ is,

  $s=\frac{a+b+c}{2}$

Then,

  $\begin{array}{c}s=\frac{4+2+5}{2}\\ =\frac{11}{2}\end{array}$

Then, the area of the triangle is,

  $\begin{array}{c}K=\sqrt{\frac{11}{2}\left(\frac{11}{2}-4\right)\left(\frac{11}{2}-2\right)\left(\frac{11}{2}-5\right)}\\ =3.799\text{square}\text{unit}\end{array}$