A parallelogram is defined as a quadrilateral in which both pairs of opposite sides are parallel and equal. These are two-dimensional shapes with parallel sides. A square is also a parallelogram since it has parallel and equal sides. Similarly, a rhombus and a rectangle also belong to the group of parallelograms. Adding adjacent angles together of parallelogram results in 180 degrees.
Some examples of parallelograms in real life are tables, street layouts on maps, boxes, building blocks, tiles, etc. While using two-dimensional shapes, we find the area for various purposes. Let us now learn in detail about the parallelograms including the area of a parallelogram.
Properties of a Parallelogram
Parallelograms have the following properties:
- The opposite sides are parallel to each other. Eg: If IJKL is a parallelogram with IJ and KL as opposite sides, then they do not intersect as they are parallel.
- If a diagonal is drawn in a parallelogram IJKL from I to K. Then it divides the parallelogram into two equal triangles.
- In any parallelogram, diagonals always bisect each other.
- Parallelogram with side lengths as x and y has perimeter equal to 2x + 2y.
- Parallelograms have consecutive angles that are supplementary.
Types of Parallelograms:
According to various factors, there are three basic types of Parallelograms. The distinguishing factors between all of these different types of parallelograms are angles, sides, etc.
- Rhombus: If ABCD is a parallelogram with sides AB = BC = CD = DA, then it’s a Rhombus.
- Square: Due to its parallel sides and bisecting diagonals, the square is considered a parallelogram.
- Rectangle: There is no doubt that a rectangle is a parallelogram since it satisfies the conditions or has the properties of parallelograms because the opposite sides are parallel, and the diagonals bisect each other.
Area and Perimeter Calculation of a Parallelogram:
Area of parallelogram: An area is a space occupied by a two-dimensional figure. The area of a parallelogram is the space enclosed by it. Parallelograms are measured in square units like cm2, m2, and inches2. They can be calculated by knowing the length of the base and the height of the parallelogram.
Look at the following parallelogram PQRS, which shows the height(h) and the base (b). The area of the parallelogram is calculated by using the following formula: Area of Parallelogram = Base (b) × Height (h)
Perimeter of Parallelogram
Perimeter is the boundary of a two-dimensional shape. The perimeter of parallelogram PQRS is the length of its boundary and hence it is equal to the sum of all its sides.
Thus, the perimeter (P) of a parallelogram with sides a and b is P = 2 (a + b) units.
Worked Example:
Example 1: Find the area and perimeter of a parallelogram whose base is 6 cm, height is 10 cm and side is 5cm.
Solution: Given, Base of parallelogram = 5 cm and Height of the parallelogram = 8 cm.
We know, Area of the parallelogram = Base x Height
Area of the parallelogram = 6 × 10
Area of the parallelogram = 60cm2.
Perimeter of the parallelogram = 2(base + side) = 2(6 + 5)
Perimeter of the parallelogram = 2(11) = 22 cm.
This is all you need to know about a parallelogram. For more solved examples and information, log on to the Cuemath website. There you can learn more about parallelogram laws and their applications in various fields.
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