Chapter 13.7, Problem 26PSC

To determine

To find: The area of the quadrilateral with given vertices.

Answer to Problem 26PSC

The area of the quadrilateral with given vertices is $120\text{units}$ .

Explanation of Solution

Given information:

The co-ordinates of vertices of the quadrilateral are $\left(-3,2\right),\left(15,6\right),\left(7,12\right)\text{and }\left(-7,8\right)$ .

Consider the following figure of the quadrilateral,

  

The area of the quadrilateral with given vertices is calculated as,

  $\begin{array}{c}A=A_r-\left(A_I+A_{II}+A_{III}+A_{IV}\right)\\ =\left(22\times 10\right)-\left(12+36+24+28\right)\\ =120\text{units}\end{array}$

Thus, the area of the quadrilateral with given vertices is $120\text{units}$ .