Chapter 11.2, Problem 26PPS

To determine

To find: The area of the quadrilateral.

Answer to Problem 26PPS

The required area is $24{\text{unit}}^2$ .

Explanation of Solution

Given:

The given vertices I $A\left(-8,6\right),B\left(-5,8\right),C\left(-2,6\right)$ and $\left(-5,0\right)$ .

Calculation:

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

  

Figure 1

The quadrilateral is in the shape of the kite.

The diagonals of the kite is calculated as,

  $\begin{array}{c}d=-2-\left(-8\right)\\ =6\end{array}$ And $\begin{array}{c}{d}_2=8-0\\ =8\end{array}$

Then, the area of the rhombus is,

  $\begin{array}{c}A=\frac{d_1{d}_2}{2}\\ =\frac{6\cdot 8}{2}\\ =\frac{48}{2}\\ =24{\text{unit}}^2\end{array}$