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Rectangle Area and Perimeter(Coordinate Geometry)
 
The area and perimeter of a rectangle can be found given the coordinates of its vertices (corners).
Try this Drag any vertex of the rectangle below. It will remain a rectangle and its dimensions calculated from its coordinates. You can also drag the origin point at (0,0).

Area

In coordinate geometry, the area of a rectangle is calculated in the usual way once the width and height are found. See Rectangle definition (coordinate geometry) to see how the width and height are found. Once the width and height are known the area is found by multiplying the width by the height in the usual way. The formula for the area is:

area = width x height

Perimeter

The perimeter of a rectangle (the total distance around the edge) is calculated in the usual way once the width and height are found. See Rectangle definition (coordinate geometry) to see how the width and height are calculated. Once the width and height are known the perimeter is found by adding twice the width to twice the height to calculate the distance around the edge of the rectangle. The formula for the perimeter is

perimeter = (2 x width) + (2 x height)

Example

The example below assumes you know how to calculate the width and height of the rectangle, as described in Rectangle (Coordinate Geometry). In the figure above, click 'reset'.
  • The height of the rectangle is the distance between the points A and B. (Using C,D will produce the same result). Here, this is 16.
  • The width is the distance between the points B and C. (Using A,D will produce the same result). Here, this is 35.
  • Area is the width times height, or 16 x 35 = 560
  • Perimeter is twice the width plus height or (2x16) + 2(35) = 102

Things to try

  1. Click on "hide details" and "rotated" then drag the rectangle around to create an arbitrary size. From the coordinates of the corner points, calculate the width, height, then area and perimeter of the rectangle. Then click on "show details" to check your result. (The results shown above are rounded off to one decimal place for clarity)
  2. Click "reset". Create a rectangle that has perimeter of approximately 80 and an area less than 60.
  3. Create a rectangle that has perimeter of approximately 80 and an area greater than 300.

Limitations

In the interest of clarity in the applet above, the coordinates are rounded off to integers and the lengths rounded to one decimal place. This can cause calculatioons to be slightly off.

For more see Teaching Notes

Other Coordinate Geometry topics