Chapter 8.4, Problem 22E

To determine

The area of quadrilateral ABCD.

Answer to Problem 22E

  $25.9$

Explanation of Solution

Given:

The given vertices are:

  

Calculation:

The area will be:

Area of triangle ABF + Area of rectangle BCEF + Area of triangle CDE

The lengths of the sides are:

  $\begin{array}{l}BF=\sqrt{{\left(1-3\right)}^2+{\left(0-\left(-2\right)\right)}^2}=\sqrt{8}=2.828\\ EF=\sqrt{{\left(-2-2\right)}^2+{\left(1-\left(-3\right)\right)}^2}=\sqrt{32}=5.65\end{array}$

Area of rectangle BCEF = $b\cdot h=\left(2.82\right)\left(5.65\right)=15.93$

The length of the sides will be:

  $\begin{array}{l}ED=\sqrt{{\left(2-4\right)}^2+{\left(-3-\left(-5\right)\right)}^2}=\sqrt{8}=2.828\\ CE=\sqrt{{\left(4-2\right)}^2+{\left(-1-\left(-3\right)\right)}^2}=\sqrt{8}=2.828\\ \text{Area of triangle CDE =}\frac{1}{2}\left(b\right)\left(h\right)=\frac{1}{2}\left(2.82\right)\left(2.82\right)=3.97\end{array}$

The area of quadrilateral ABCD will be:

  $\begin{array}{l}=6+15.93+3.97\\ =25.9\end{array}$