Question

The coordinates of the vertices of rectangle ABCD are A(2,2), B(2,6), C(8,6), and D(8,2). What is the area in square units of rectangle ABCD?

Answer 1

The area of a rectangle is the product of two perpendicular sides.

Let `bar(AB)` and `bar(AD)` be the measure of the vertical and horizontal side, correspondingly.

By the formula of the distance between two points on a plain:

`bar(AB)=sqrt((x_B-x_A)^2+(y_B-y_A)^2)`

`bar(AB)=sqrt((2-2)^2+(6-2)^2)=4`

`bar(AD)=sqrt((8-2)^2+(2-2)^2)=6`

The area of the rectangle is given by:

`A_[ABCD]=bar(AB)timesbar(AD)=4times6=24` units square

Answer 2

24 sq units

Explanation:

The diagram of the rectangle as described is shown below

As seen therefrom, length is 6 units and the width is 4 units. The area would therefor be 24 sq units