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).

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

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)

**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

- 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)
- Click "reset". Create a rectangle that has perimeter of approximately 80 and an area less than 60.
- Create a rectangle that has perimeter of approximately 80 and an area greater than 300.

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

- Introduction to coordinate geometry
- The coordinate plane
- The origin of the plane
- Axis definition
- Coordinates of a point
- Distance between two points

- Introduction to Lines

in Coordinate Geometry - Line (Coordinate Geometry)
- Ray (Coordinate Geometry)
- Segment (Coordinate Geometry)
- Midpoint Theorem

- Cirumscribed rectangle (bounding box)
- Area of a triangle (formula method)
- Area of a triangle (box method)
- Centroid of a triangle
- Incenter of a triangle
- Area of a polygon
- Algorithm to find the area of a polygon
- Area of a polygon (calculator)
- Rectangle
- Square
- Trapezoid
- Parallelogram

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