A parallelogram is a 2-dimensional shape that has four sides and has two pairs of parallel lines. The parallelogram consist of equal opposite sides and its opposite angles are equal in measure. Let us now discuss the parallelogram formula i.e. area and perimeter of the parallelogram.
What is a Parallelogram?
A parallelogram is a quadrilateral that has two pairs of parallel and equal sides. A quadrilateral is said to be a parallelogram if the two pairs of opposite sides in a quadrilateral are equal, then it is a parallelogram.
If two opposite sides in a quadrilateral are parallel and equal, then this quadrilateral is a parallelogram; if, in a quadrilateral, the diagonals bisect each other, then this quadrilateral is a parallelogram.
Properties of Parallelogram
There are some important properties of parallelograms:
- In a parallelogram opposite sides are equal
- In a parallelogram opposite angels are equal.
- The sum of adjacent angles are supplementary i.e. (∠B + ∠C = 180°).
- In a parallelogram, if one angle is right, then all angles are right.
- Diagonals of a parallelogram bisect each other.
- In a parallelogram, each diagonal of a parallelogram divides it into two congruent triangles.
The Perimeter of a Parallelogram
The perimeter is the sum of the length of all the 4 sides. In a parallelogram opposite sides are equal so the perimeter is:
P = 2b + 2a
P = 2( a + b)
|a||Length of the side of the parallelogram|
|b||Length of the side of the parallelogram|
Area of Parallelogram
The area of a parallelogram is the number of square units inside the polygon. The area of a parallelogram can be determined by multiplying the base and height. For finding the area of a parallelogram, the base and height must be perpendicular. The area of a parallelogram is given by
Area =b × h
|b||Base of Parallelogram|
|h||The altitude of the parallelogram|
Derivation of Area of Parallelogram
Let ABCD be the parallelogram whose area is being derived. We extend AB to F such as F as the foot of the altitude from C. Now, construct the point E such that DE is the altitude from D.
In \(\Delta AED AND \Delta BFC\)
AD = BC
\(\angle AED = \angle BFC\)
DE = CF
\(\Delta AED \cong \Delta BFC\)
area \( (\Delta AED)= area (\Delta BFC) \)
Area (ABCD) = EF ͯ FC = AB ͯ CF
Q.1: Find the area of a parallelogram with a base is 10 cm and a height is 5 cm.
Solution: Given, Base = 10 cm, Height = 5 cm
Area of Parallelogram = B × H
Area = (10 cm) ͯ× (5 cm)
Area = 50 cm2
Therefore, Area of Parallelogram is 60 cm2.
Q.2: Find the perimeter of a parallelogram whose base is 20 cm and height 12 cm?
Base = 20 cm
Height = 12 cm
Perimeter of a Parallelogram = 2(Base + Height)
= 2(20 + 12)
= 2 × 32 cm
= 64 cm
Therefore, Perimeter of a Parallelogram is 64 cm