Question

What is the perimeter of quadrilateral ABCD?

Answer 1

Using distance(D) formula for two points is given by:

`D = √((x_1-x_2)^2+(y_1-y_2)^2)`

From the given figure:

The coordinates of the quadrilateral ABCD are:

A(-3, 2), B(4, 2), C(3, -3) and D(-3, -3)

For A(-3, 2) and B(4, 2)

using formula we have;

`AB= √((-3-4)^2+(2-2)^2)`

⇒
`AB= √((-7)^2+(0)^2)`

⇒
`AB= √(49) =7` units

Similarly;

For B(4, 2) and C(3, -3)

`BC= √((4-3)^2+(2-(-3))^2)`

⇒
`BC= √((1)^2+(5)^2)`

⇒
`BC= √(1+25)=√(26)` units.

For C(3, -3) and D(-3, -3)

`CD= √((3-(-3))^2+(-3-(-3))^2)`

⇒
`CD= √((6)^2+(0)^2)`

⇒
`CD= √(36+0)=√(36)=6` units.

For A(-3, 2) and D(-3, -3)

`AD= √((-3-(-3))^2+(2-(-3))^2)`

⇒
`AD= √(0+25)=√(25)=5` units.

Perimeter is equal to the sum of all the sides of quadrilateral ABCD:

Perimeter = AB+BC+CD+AD

then;

`\text{Perimeter} = 7+√(26)+6+5 = 18+√(26)` units

Therefore, the perimeter of quadrilateral ABCD is,
`18+√(26)` units