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?

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Answer 1 · 2018-02-01T16:35:08

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

Let $¯ ¯¯¯¯ ¯ A B$ $bar(AB)$ and $¯ ¯¯¯¯ ¯ A D$ $bar(AD)$ be the measure of the vertical and horizontal side, correspondingly.

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

$¯ ¯¯¯¯ ¯ A B = \sqrt{{(x_{B} - x_{A})}_{B}^{2} + {(y_{B} - y_{A})}_{B}^{2}}$ $bar(AB)=sqrt((x_B-x_A)^2+(y_B-y_A)^2)$

$¯ ¯¯¯¯ ¯ A B = \sqrt{{(2 - 2)}^{2} + {(6 - 2)}^{2}} = 4$ $bar(AB)=sqrt((2-2)^2+(6-2)^2)=4$

$¯ ¯¯¯¯ ¯ A D = \sqrt{{(8 - 2)}^{2} + {(2 - 2)}^{2}} = 6$ $bar(AD)=sqrt((8-2)^2+(2-2)^2)=6$

The area of the rectangle is given by:

$A_{A B C D} = ¯ ¯¯¯¯ ¯ A B \times ¯ ¯¯¯¯ ¯ A D = 4 \times 6 = 24$ $A_[ABCD]=bar(AB)timesbar(AD)=4times6=24$ units square

Answer 2 · 2018-02-01T16:36:42

24 sq units

The diagram of the rectangle as described is shown below

enter image source here

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