Area of Parallelogram

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Parallelogram Introduction

Parallelogram is a type of polygon, whose opposite sides are parallel to each other. It is a two dimensional geometric figure (also known as quadrilateral), where the pair of parallel sides are similar in length, Parallelogram can also be defined as a quadrilateral that has equal and parallel opposite sides. Example: Let ABCD be a quadrilateral whose side AD = BC and AB = CD along with that side AB parallel to CD and AD parallel to BC.


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In the given figure side AB is equal to side CD, side BC is equal to side AD and side AB is parallel to side CD and side BC is parallel to side AD. From the above given figure it is clear that quadrilateral ABCD is a parallelogram. As parallelogram is a two-dimensional figure, it has area and perimeter, In this article, we will discuss area of parallelogram in detail.


What is the Area of Parallelogram?

Area of a parallelogram can be defined as the area bounded by the parallelogram in a given two-dimensional base. To recall, a parallelogram is a special type of quadrilateral having  four sides and pairs of opposite sides are parallel and equal to each other. As both rectangle and parallelogram have the same properties, it can be said that area of parallelogram is equal to area of rectangle.


How to Find Area of Parallelogram

To find the area of parallelogram, we use a specific formula for that. Let ABCD be a parallelogram. So area of parallelogram can be written as:  base × height.


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So from the above figure it is clear that height is the perpendicular distance from the base of parallelogram. Suppose in any figure, we have the area of the parallelogram and base of the parallelogram then we can find out the height of the parallelogram.


Formula for finding different measurement of parallelogram:

Area =  base × height

Base = area / height

Height = area / base


Perimeter of Parallelogram

Perimeters of any shape can be defined as the total length of that shape. In the same way we can define the perimeter of parallelogram i.e the total length of boundaries of parallelogram. If we add both length and breadth of parallelogram then we can find out the perimeter of parallelogram.


Formula to find perimeter of parallelogram is:

Perimeter = 2(l + b)


Area of Parallelogram Based on Different Bases

If the given figure of two parallelograms are there and both have the same base and are between the same lines then the area of both parallelograms will be the same as they have the same base.


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From the above figure we can find out that both ABCD and FBCE are parallelogram and both of them have the same base i.e. BC between two parallel lines AB and EC.


Due to same base we concluded that:

Area of parallelogram ABCD = Area of parallelogram FBCE.

Conclusion: The parallelograms having the same base and equal area must lie between the same parallels.


Proof:

Two parallelograms ABCD and FBCE, on the same base BC and between the same parallel line AB and EC.

To prove: Area of Parallelogram (ABCD) = Area of Parallelogram (FBCE).

Consider the figure given above:

Parallelogram ABCD and FBCE are on the same base and between the same parallels AB and EC.

Hence, we can conclude that

Area of parallelogram ABCD = Area of parallelogram FBCE.


Different Properties of Parallelogram Based on its Sides and Angles

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From the above figure we know that:

Side AB = CD, AD = BC……….(1)

Along with sides And, ∠A = ∠C & ∠B = ∠D…………..(2)

At the same time , ∠A & ∠D are supplementary to each other as these interior angles lie on the same side of the transversal. Similarly And, ∠C & ∠B  are supplementary to each other.


So from above theory it can be concluded that:

∠A + ∠D = 180……….(3)

∠B + ∠C = 180…………(4)

From above equation 1, 2, 3 and 4 are considered as properties of parallelogram.


More Basic Properties of parallelogram:

Some of the basic properties of parallelogram are listed below:

  • The opposite sides of parallelogram are congruent in nature.

  • The opposite angles of parallelogram are congruent in nature.

  • The consecutive angles of parallelogram are supplementary in nature.

  • If anyone of the angles is a right angle, then all the other angles will be the right angle as the sum of opposite angles are 180 degree.

  • The two diagonals of parallelogram bisect each other.

  • Each diagonal bisects the parallelogram into two congruent triangles.

FAQ (Frequently Asked Questions)

1. Is a Rectangle a Parallelogram?

Ans. Yes, a rectangle is also a parallelogram, because it follows all the conditions needed to follow the properties of parallelogram such as the opposite sides are parallel and diagonals intersect at 90°.

2. What is the Difference Between Parallelogram and Trapezium?

Ans. The main point of difference between a parallelogram and triangle is that in case of parallelogram both pairs of opposite sides are parallel while in case of trapezium only one pair of opposite sides is parallel.

3. What is the Perimeter of a Parallelogram?

Ans. Formula to find perimeter of parallelogram is:

Perimeter = 2(l + b)

4. List the Properties of Diagonals of Parallelogram?

Ans. The two diagonals of parallelogram bisect each other. Each diagonal bisects the parallelogram into two congruent triangles.