A parallelogram is a two-dimensional quadrilateral having two opposite sides parallel and equal to each other. The area of parallelogram is the space enclosed by its four sides. It is measured in square units according to the units used to measure the sides of the parallelogram such as centimeters, meters, inches, etc. This means if the sides of a parallelogram are measured in inches, the area will be measured in square inches.
Calculation of the Area of a Parallelogram
The area of a parallelogram can be calculated using the dimension of its base and height. The base is the bottom side of the parallelogram and the height is the perpendicular distance between the base and its opposite side. The formula for calculation of the area of a parallelogram is given as:
Area of parallelogram = Base * Height
So, if the dimension of the base of a parallelogram is ‘b’ and the height or altitude is ‘h’, then the area of the parallelogram, A = b * h
Let’s consider a parallelogram PQRS with its base as SR and the opposite side of the base in PQ. A perpendicular line is drawn on the base from point P which meets the base SR at O. Therefore PO can be considered as the height of the parallelogram PQRS. Now, the area of this parallelogram can be calculated using the following formula:
Area (A) = Base (b) X Height (h)
If the base PQ = 20 cm and the height PO is measured as 7 cm, the area of parallelogram PQRS will be:
A = b X h = 20 cm X 7 cm = 140 square cms
A parallelogram is a polygon with four sides in which two opposite sides are parallel and equal to each other. The name signifies that it is a shape formed by parallel sides. The adjacent sides may or may not be equal and the angle formed by the adjacent sides may vary but the pair of opposite sides are always equal and parallel to each other.
Types of Parallelograms
Different geometrical shapes satisfy the criteria of parallelogram but are named differently depending on the types of angles formed by the adjacent sides and the dimension of the sides. These are explained as follows:
- Rectangle: This is a special type of parallelogram in which the adjacent sides are not equal but the angles formed by them are 90 degrees. In other words, a parallelogram with unequal adjacent sides and all four interior angles at 90 degrees is called a rectangle.
- Square: It is a parallelogram with all sides equal to each other and angles formed by adjacent sides are 90 degrees.
- Rhombus: This is a parallelogram in which all sides are equal but neither of the interior angles is 90 degrees.
Properties of Parallelogram
- The two pairs of opposite sides of a parallelogram are parallel
- The two pairs of opposite sides of a parallelogram are equal to each other
- The two diagonals of a parallelogram bisect each other
- The opposite interior angles of a parallelogram are equal
- The two consecutive angles of a parallelogram are supplementary
Identification of a Parallelogram
A parallelogram is a special type of quadrilateral with two opposite sides parallel and equal in dimension. So the easy way to identify a parallelogram is to ensure that it’s both pairs of opposite sides are equal and parallel to each other. The angles formed by adjacent sides of a parallelogram can be different according to the shape of the parallelogram.
Let’s consider a quadrilateral ABCD such that AB and DC are parallel and AB = DC. Again, AD and BC are parallel and AD = BC. Therefore ABCD is called a parallelogram.
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