Chapter 6, Problem 35RE

To determine

To find: the area of the given triangle.

Answer to Problem 35RE

The area of the triangle $=8.356\text{ square units,}$

Explanation of Solution

Given information:

Consider $a=12.3,b=15.8,c=3.7$

Formula used:

Heron’s formula :

Perimeter of triangle $s=\frac{a+b+c}{2}$

Area of the triangle $A=\sqrt{s(s-a)(s-b)(s-c)}$

Where, $a,b,c$ are side lengths.

Calculation:

From the given data,

  $s=\frac{12.3+15.8+3.7}{2}=\frac{32.8}{2}=15.9$

  $\begin{array}{l}A=\sqrt{15.9\left(15.9-12.3\right)\left(15.9-15.8\right)\left(15.9-3.7\right)}=\\ =\sqrt{15.9\left(3.6\right)\left(0.1\right)\left(12.2\right)}\\ =8.356\text{ square units,}\end{array}$

Hence, the area of the triangle $=8.356\text{ square units,}$