This page describes how to derive the formula for the area of a parallelogram. It works by moving a piece of the parallelogram so as to make a rectangle with the same area, which is easier to calculate.

- Start with a parallelogram with known
base
length (width)
*w*and altitude*h*(height). - Cut off a triangular section.
- Translate (move) the copy to touch the original so as to create a rectangle.

Click on the "Run" button below to see this in action.

This rearranging has created a rectangle whose area is clearly the same as the original parallelogram.
Recall that the
area of a rectangle is found by multiplying its width times its height. The area of the original parallelogram is therefore
where
*w* is the width, or length of a base, and

*h* is the altitude (height) of the parallelogram.

- Polygon general definition
- Quadrilateral
- Regular polygon
- Irregular polygon
- Convex polygons
- Concave polygons
- Polygon diagonals
- Polygon triangles
- Apothem of a regular polygon
- Polygon center
- Radius of a regular polygon
- Incircle of a regular polygon
- Incenter of a regular polygon
- Circumcircle of a polygon
- Parallelogram inscribed in a quadrilateral

- Square
- Diagonals of a square
- Rectangle
- Diagonals of a rectangle
- Golden rectangle
- Parallelogram
- Rhombus
- Trapezoid
- Trapezoid median
- Kite
- Inscribed (cyclic) quadrilateral

- Regular polygon area
- Irregular polygon area
- Rhombus area
- Kite area
- Rectangle area
- Area of a square
- Trapezoid area
- Parallelogram area

- Perimeter of a polygon (regular and irregular)
- Perimeter of a triangle
- Perimeter of a rectangle
- Perimeter of a square
- Perimeter of a parallelogram
- Perimeter of a rhombus
- Perimeter of a trapezoid
- Perimeter of a kite

- Exterior angles of a polygon
- Interior angles of a polygon
- Relationship of interior/exterior angles
- Polygon central angle

- Tetragon, 4 sides
- Pentagon, 5 sides
- Hexagon, 6 sides
- Heptagon, 7 sides
- Octagon, 8 sides
- Nonagon Enneagon, 9 sides
- Decagon, 10 sides
- Undecagon, 11 sides
- Dodecagon, 12 sides

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