Question

In the figure, ABCD is a parallelogram.
(a) Write the co-ordinates of D.
(b) What is the height of this parallelogram?
(c) Find the perimeter and area of it.

Answer 1

(a) Distance between A and B = |4 - 0| = 4
Since the opposite sides of a parallelogram are equal, the distance between C and D is also 4.
Also, the y-coordinates of A and B are equal, the side AB is parallel to the x-axis. And, since ABCD is a parallelogram, CD is also parallel to the x-axis. So the y-coordinates of C and D are also equal.
Thus, the x-coordinate of D = 8 - 4 = 4
Hence, the coordinates of D are (4, 5).
(b) The x-coordinates of D and B are equal. So the line BD is parallel to the y-axis or BD is perpendicular to the x-axis.
So, height of the parallelogram $=DB=|y_1-y_2|=|5-2|=|3|=3$
(c) $BC=\sqrt{(x_1-x_2{)}^2+(y_1-y_2{)}^2}$
$=\sqrt{(8-4{)}^2+(5-2{)}^2}$
$=\sqrt{\left(4^2\right)+(3{)}^2}$
$=\sqrt{16+9}$
$=\sqrt{25}$
= 5 units
AD = BC = 5 units
Perimeter $=2\times (4+5)=18units$
$Area=Base\times Height=4\times 3=12sq.units.$