Answer:
Find the length of sides. The sum of these sides is the perimeter of a quadrilateral
Step-by-step 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 =[tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex] where
[tex]x_{1}= 1,x_{2}=4, y_{1}=3, y_{2}=2[/tex]
Substituting values we get,
AB=[tex]\sqrt{(4-1)^2+(2-3)^2 }[/tex]
AB=[tex]\sqrt{(3)^2+(-1)^2 }[/tex]
AB=[tex]\sqrt{(9+1 }[/tex]
AB=[tex]\sqrt{10}[/tex]
Similarly, we can find length of BC,CD and DA
BC=[tex]\sqrt{5}[/tex] ,CD=[tex]\sqrt{5}[/tex] ,DA=2
Then sum of these sides is perimeter of quadrilateral=[tex]12+2\sqrt{5}[/tex]
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.
