Chapter 1.8, Problem 20E

To determine

To calculate: The area of the parallelogram and its figure on coordinate plane.

Answer to Problem 20E

The area of the parallelogram is $\text{16 sq}\text{. units}$ and its figure is,

  

Explanation of Solution

Given information:

The four vertices of the parallelogram $\text{A}\left(1,2\right),\text{B}\left(5,2\right),\text{C}\left(3,6\right)\text{ and D}\left(7,6\right)$ .

Formula used:

Area of a parallelogram is the product of its base and height. So, if b is the base and h is its height, area of parallelogram is calculated as,

  $\text{A}=b\cdot h$

Calculation:

Consider the given four vertices of the parallelogram $\text{A}\left(1,2\right),\text{B}\left(5,2\right),\text{C}\left(3,6\right)\text{ and D}\left(7,6\right)$ .

Observe that all the points lie in the first quadrant of the coordinate plane, so, plot the points in first quadrant of the coordinate plane and join the vertices to form the parallelogram as,

  

In the above figure, it is observed that the base of parallelogram is 4 units and its height is 4 units.

Recall that the area of a parallelogram is the product of its base and height. So, if b is the base and h is its height, area of parallelogram is calculated as,

  $\text{A}=b\cdot h$

Apply it,

  $\begin{array}{c}\text{A}=b\cdot h\\ =4\cdot 4\\ =16\text{ sq}\text{. units}\end{array}$

Thus, area of the parallelogram is $16\text{ sq}\text{. units}$ and its figure is,