Question

The vertices of a quadrilateral in the coordinate plane are known.How can the perimeter of the figure be found?

Answer 1

Find the length of sides. The sum of these sides is the perimeter of a quadrilateral

Explanation:

A quadrilateral is a figure that has four sides. To find the perimeter of any quadrilateral, we find the sum of all four sides.

Given:

The co-ordinates of all vertices of a quadrilateral is known

To Find:

Perimeter of a quadrilateral

Steps:

1. Find the length of all sides using the straight line distance formula.

2. Add all the sides to find perimeter.

Let us take an example:

In figure the four co-ordinates are as follows:

A(1,3), B(4,2), C(3,0) and D(1,1)

Perimeter of quadrilateral ABCD= AB+BC+CD+DA

To find AB we use straight line distance formula, which is as follows:

AB =
`\sqrt{(x_(2)-x_(1))^2+(y_(2)-y_(1))^2 }` where

`x_(1)= 1,x_(2)=4, y_(1)=3, y_(2)=2`

Substituting values we get,

AB=
`√((4-1)^2+(2-3)^2 )`

AB=
`√((3)^2+(-1)^2 )`

AB=
`√((9+1 )`

AB=
`√(10)`

Similarly, we can find length of BC,CD and DA

BC=
`√(5)` ,CD=
`√(5)` ,DA=2

Then sum of these sides is perimeter of quadrilateral=
`12+2√(5)`

Note: In this example, the perimeter cam out in roots, due to the values of co-ordinates taken. But the sum can also be a whole number.