Chapter 15, Problem 23CR

To determine

To Find: The area of the polygon.

Answer to Problem 23CR

  $36unit{s}^2$

Explanation of Solution

Given:

  

  $\begin{array}{l}BC=4\\ CD=3\\ AB=12\\ AD=13\end{array}$

Formula Used:

  $\text{Area of triangle }=\frac{1}{2}bh$

Calculation:

  $\begin{array}{l}BC=4\\ CD=3\\ AB=12\\ AD=13\\ \text{Area of triangle }=\frac{1}{2}bh\\ \text{Join }AC\\ ar\left(\Delta BCD\right)=\frac{1}{2}\times 3\times 4=6\\ BD=5\text{By pythagorean triple}\\ ar\left(\Delta BDA\right)=\frac{1}{2}\times 5\times 12=30\\ \text{Area of polygon}=ar\left(\Delta BCD\right)+ar\left(\Delta BDA\right)\\ =6+30\\ =36unit{s}^2\end{array}$

Conclusion:

Thus, the area of polygon is $36unit{s}^2$