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What Is a Parallelogram? (Mathematics Lesson)

What Is a Parallelogram

A paralleogram is a four sided shape with opposite sides parallel and equal in length.

Properties of Parallelograms

  • Opposite sides of a parallelogram are parallel.


  • Opposite sides of a parallelogram are of equal length.


  • Opposite angles of a parallelogram are equal.


  • Adjacent angles of a parallelogram add up to 180°. They are supplementary angles.


  • All angles of a parallelogram add up to 360°.


  • The diagonals of a parallelogram bisect each other. The diagonals cross each other half-way along their lengths.

The Perimeter of a Parallelogram

The perimeter of a parallelogram is given by the formula:



where of b is the length of the base and s is the length of the side of the parallelogram.

The Area of a Parallelogram

The area of a parallelogram is given by the formula:



where b is the length of the base and h is the height of the parallelogram.

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Note
WHAT'S IN A NAME?

Parallelogram comes from the Greek word 'parallelogrammon' meaning 'parallel sides'.

A PARALLELOGRAM IS A POLYGON

A parallelogram is a type of polygon.

A polygon is a 2-dimensional shape with straight sides.

A parallelogram is an irregular polygon. Irregular polygons have different length sides and different angles.

A PARALLELOGRAM IS A QUADRILATERAL

A parallelogram is a quadrilateral.

A quadrilateral is a four-sided polygon.

Squares, rectangles and trapezoids are also quadrilaterals.

INTERIOR ANGLES OF A PARALLELOGRAM

A parallelogram is a four-sided polygon. The sum of the interior angles of an n-sided polygon is is: (n - 2) × 180°

This means the interior angles of a polygon add up to:

(4 - 2) × 180° = 360°

This is the case for all quadrilaterals, such as squares, rectangles and trapezoids.

AREAS OF PARALLELOGRAMS AND RECTANGLES

The formula for the area of a parallelogram is the same as for the area of a rectangle. Can you see why from the image below?