Let's have formula for area of a parallelogram & some examples:
A formula will show how to find the area of a parallelogram. The standard formula for area of a parallelogram is given as Area = B x H where B is the base and H is the height of a parallelogram.
Figure given above shows that base and height have to be at right angles to each other for finding the area of a parallelogram. The same formula of area of a parallelogram can be applied to all types of parallelogram like rhombus, square, rectangles and others. Now lets have an example of it.
(1) Find the area of a parallelogram if base is equal to 5cms and its height is 4cms:
Area = B x H = 5 x 4 = 20cm2.
(2) Find the area of a square with length 6cms.
We know that square is a parallelogram with all sides and angles are equal. Hence base and height are same. Therefore Area = 6 x 6 = 36cm2.
(3) Find the area of a rectangle with width 6cms and height 4cms:
Area = 6 x 4 = 24cm2.
(4) Find the area of a rhombus with height 7cms and base 8cms:
Area = B x H = 8 x 7 = 56cm2.
Formula to find the area of a parallelogram vectors:
To find the area of a parallelogram vectors, consider two vectors u and v as the adjacent sides of a parallelogram being shown below. The height can be given as |v| |sin θ| where θ is angle between two vectors.
So how do you find the area of a parallelogram for vectors? Lets apply same standard formula for area. Area = B x H = |u| |v| sin θ = |u x v|. This shows that the direction of cross product can be given by the right-hand rule while the magnitude is given by area of parallelogram for two vectors.
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