Parallelogram - Math Is Fun

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Parallelogram

(Jump to Area of a Parallelogram or Perimeter of a Parallelogram)

A parallelogram is a flat shape with opposite sides parallel and equal in length.

Parallelogram labeled with opposite angles A and B, showing sides parallel

  • Opposite sides are parallel
  • Opposite sides are equal in length
  • Opposite angles are equal (angles A are the same, and angles B are the same)
  • Angle A and angle B add up to 180°, so they are supplementary angles

Play with a parallelogram:

images/geom-quad.js?mode=parallelogram

NOTE: Squares, Rectangles and Rhombuses are all parallelograms!

Rectangle with right angles shown, illustrating it as a special parallelogram

Example:

A parallelogram where all angles are right angles is a rectangle!

Area of a Parallelogram

Parallelogram with base 'b' and perpendicular height 'h' labeled

The Area is the base times the height:

Area = b × h

Note: The height (h) is at right angles to the base (b), not the sloped side!

Example: A parallelogram has a base of 6 m and is 3 m high, what is its Area?

Area = 6 m × 3 m = 18 m2

Perimeter of a Parallelogram

The Perimeter is the distance around the edges.

Parallelogram with base 'b' and adjacent side 's' labeled for perimeter calculation

The Perimeter is 2 times the (base + side length):

Perimeter = 2(b+s)

Example: A parallelogram has a base of 12 cm and a side length of 6 cm, what is its Perimeter?

Perimeter = 2 × (12 cm + 6 cm) = 2 × 18 cm = 36 cm

Diagonals of a Parallelogram

Parallelogram with its two diagonals drawn, intersecting at their midpoints

The diagonals of a parallelogram bisect each other.

In other words the diagonals intersect each other at the half-way point.

Pantograph

Based on a parallelogram, a pantograph can be used to duplicate and resize an image by tracing.

Pantograph drawing tool with multiple hinged arms forming parallelograms

Inside Any Quadrilateral

And there is a parallelogram in any quadrilateral.

9121, 9122, 9123, 9124, 9125, 9126, 9127, 9128, 9129, 9130 Quadrilaterals Geometry Index

Tag » How Many Degrees In A Parallelogram