Parallelogram And Rectangle

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Why are the formulas for the area of a parallelogram and the area of a rectangle the same? Move the slider from left to right to see the parallelogram dissected and the pieces reassembled in the form of a rectangle.

Parallelogram

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

  1. A rectangle is a parallelogram with equal angles. So, this means a rectangle has inherited all the properties of a parallelogram and in addition to that it is having all angles equal. Here, AB = CD and BC = AD. And ∠A =∠B = ∠C = ∠D (All angles are equal).
  2. In the diagram to the above, the parallelogram and rectangle share a vertex (D), one vertex of the rectangle (E) is on a side of the parallelogram, and one vertex of the parallelogram (C) is on a side of the rectangle. That is enough information to guarantee that the rectangle and parallelogram have equal area. Here’s an argument why.
  3. » parallelogram, rectangle, and rhombus » parallelogram and rectangle » rectangle only 2 See answers AnonymousHelper1807 AnonymousHelper1807 Answer: D. Step-by-step explanation: It's only a rectangle. It can not be a parallelogram neither a rhombus nor a square.

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


and show equal sides

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)
Angles 'a' and 'b' add up to 180°, so they are supplementary angles.

Play with a Parallelogram:

Parallelogram

Rectangle And Parallelogram Similarities

NOTE: Squares, Rectangles and Rhombuses are all Parallelograms!

Example:

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

Area of a Parallelogram

The Area is the base times the height:

Area = b × h

(h is at right angles to b)

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.

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

Parallelogram And Rectangle Differences

Diagonals of a Parallelogram

The diagonals of a parallelogrambisect each other.

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

Inside Any Quadrilateral

Parallelogram And Rectangle Area

And there is a parallelogram in any quadrilateral.