Chapter 11.2, Problem 27PPS

To determine

To find: The area of the quadrilateral.

Answer to Problem 27PPS

The required area is $18{\text{unit}}^2$ .

Explanation of Solution

Given:

The given vertices I $W\left(3,0\right),X\left(0,3\right),Y\left(-3,0\right),Z\left(0,-3\right)$ .

Calculation:

Consider the graph for the given vertices is shown in Figure 1

  

Figure 1

The quadrilateral is in the shape of the rohmbus.

The diagonals of the rohmbusis calculated as,

  $\begin{array}{c}{d}_1=3-\left(-3\right)\\ =6\end{array}$ And $\begin{array}{c}{d}_2=3-\left(-3\right)\\ =6\end{array}$

Then, the area of the rhombus is,

  $\begin{array}{c}A=\frac{d_1{d}_2}{2}\\ =\frac{6\cdot 6}{2}\\ =\frac{36}{2}\\ =18{\text{unit}}^2\end{array}$