Chapter 6.1, Problem 62E

To determine

To find: the area of the triangle.

Answer to Problem 62E

  $21.3\text{ square inch}$

Explanation of Solution

Given information:

Let the sides of triangle be $a,b$ and $c$ .

  $\begin{array}{l}a=6\text{ inches}\\ b=8\text{ inches}\\ c=12\text{ inches}\end{array}$

Calculation:

The semi perimeter of the triangle will be evaluated as follows:

  $\begin{array}{c}s=\frac{1}{2}\left(a+b+c\right)\\ =\frac{1}{2}\left(6+8+12\right)\left[\text{Put the values of }a,b\text{ and }c\right]\\ =\frac{1}{2}\left(26\right)\\ =13\text{ inches}\end{array}$

Now put the values in the Heron’s formula and evaluate the area of triangle as shown below.

  $\begin{array}{c}A=\sqrt{s\left(s-a\right)\left(s-b\right)\left(s-c\right)}\\ =\sqrt{13\left(13-6\right)\left(13-8\right)\left(13-12\right)}\\ =\sqrt{455}\\ =21.3\text{ square inch}\end{array}$

Thus the area of triangle is $21.3\text{ square inch}$ .