THE AREA OF PARALLELOGRAM

Parallelogram

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:

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

Diagonals of a Parallelogram

The diagonals of a parallelogram bisect each other.

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

Calculate the Area of parallelogram formed by vectors

Area of parallelogram formed by vectors calculator

Select how the parallelogram is defined:

Parallelogram is defined:   by two vectors  by coordinates of points 

Type the values of the vectors:

 = {, 

, 

}

 = {, 

, 

}

You can input only integer numbers, decimals or fractions in this online calculator (-2.4, 5/7, ...). More in-depth information read at these rules.

Solution:

A = |a × b|

Calculate cross product of vectors:

c = a × b

a × b = ijka_xa_ya_zb_xb_yb_z = ijk000000 = i (0·0 - 0·0) - j (0·0 - 0·0) + k (0·0 - 0·0) = i (0 - 0) - j (0 - 0) + k (0 - 0) =

 = {0; 0; 0}

Calculate magnitude of a vector:

|c| = √c_x² + c_y² + c_z² = √0² + 0² + 0² = √0 + 0 + 0 = √0 =  0

Calculate parallelogram area:

A

=  0