In mathematics, we generally define a parallelogram as a figure which is two-dimensional and consists of four sides. The properties of a parallelogram are similar to that of a rectangle; thus we can consider that a parallelogram is a type of a rectangle. The area of a parallelogram can be defined as a space or region which is enclosed by the sides of the parallelogram. Mathematically, the area of parallelogram is given by ‘b’ * ‘h’ where b is the base of the parallelogram and h is the height of the parallelogram respectively. In this article, we may try to cover some topics related to the area of parallelogram such as the different ways of calculating area and calculations based on it.
Parallelogram
A parallelogram can be defined as a unique type of quadrilateral which is enclosed by parallel lines. In other words, parallelogram has been derived from a Greek word that basically signifies any structure which is bounded or enclosed by parallel lines. You might have observed various objects in your everyday life such as a kite, a matchbox, or a table, all these objects are examples of parallelograms. The above-mentioned few lines also signify that a parallelogram can be of various types such as a rhombus, a rectangle, a square, etc.
Some Important Properties of a Parallelogram
There are various important properties of a parallelogram but few of them are mostly used in calculations based on parallelograms. The following points mentioned below analyses some of the significant properties of a parallelogram.
- In a parallelogram, the sides opposite are parallel and congruent to each other.
- In a parallelogram, the angles which are opposite are also congruent and the angles which are consecutive are supplementary.
- There is a very unique fact or you could say a characteristic that if any angle is right-angled or exactly measures 90 degrees, then every other angle will also measure about 90 degrees and thus be called a right-angled parallelogram.
- The diagonals of a parallelogram bisect each other and also result in the formation of two different congruent triangles.
- The parallelogram law states that the addition of the square of every side ( four ) of a parallelogram is equal to the sum or addition of the square of the diagonal.
Area of Parallelogram Using the Base And Height
One of the most common ways of calculating the area of a parallelogram is doing it with the help of the sides or base and height of the parallelogram. The area of parallelogram is the space that is enclosed or covered by the sides of it in a plane that is two-dimensional. Mathematically, the formula given for the are is ‘b’ * ‘h’ where b is the base and h is the height of the parallelogram. In order to understand this concept in a detailed manner we must solve some examples related to it;
Example 1:
Find the area of parallelogram provided that the base ‘b’ is 5 cm and ‘h’ is 10 cm?
Provided that,
Base of the parallelogram = 5 cm
Height of the parallelogram = 10 cm
Using the formula of area of parallelogram, b * h
5 * 10 = 50 cm
Thus, the area of parallelogram is 50 cm.
Example 2:
Find the area of parallelogram provided that the base ‘b’ is 6 cm and ‘h’ is 5 cm?
Provided that,
Base of the parallelogram = 6 cm
Height of the parallelogram = 5 cm
Using the formula of area of parallelogram, b * h
6 * 5 = 30 cm
Thus, the area of parallelogram is 30 cm.
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