Question

How do you use coordinates to find the perimeter and area of polygons?

Answer 1

Explanation:

Make a table with the x,y coordinates of each vertex.

Vertical left side of the table A ,B,C D.. A again (From top to bottom)

Horizontal top of the table : x,y( From left to right)

Start at any vertex and go around the polygon in either direction.

Add the starting vertex again at the end.

Combine the first two rows by:

Multiplying the first row x by the second row y

Multiplying the first row y by the second row x

Subtract the second product form the first.

Repeat this for rows 2 and 3, then rows 3 and 4 and so on.

Add these results, make it positive if required, and divide by two.

Answer 2

First, number the vertices in order, going either clockwise or counter-clockwise, starting at any vertex.The area is then given by the formula. Where x1 is the x coordinate of vertex 1 and yn is the y coordinate of the nth vertex etc. Notice that the in the last term, the expression wraps around back to the first vertex again! Hope this helped.