What is a Parallelogram?
A parallelogram is a two dimensional shape. It is a special case of quadrilaterals where both pairs of opposite sides are parallel and equal in length as shown in the image.
Properties of a Parallelogram
- The opposite sides are equal in length.
- The opposite angles are equal.
- The consecutive angles of a parallelogram are supplementary to each other.
- The diagonals of a parallelogram bisect each other.
- The diagonals divide a parallelogram into two triangles that are congruent to each other.
Special Parallelograms
There are also special types of parallelograms that have similar characteristics to a parallelogram. These special parallelograms are:
- Rectangle
- Rhombus
- Square
Let’s look at the definition of such special parallelograms.
- Rectangle : A parallelogram with each angle equal to 90° is called a rectangle.
- Rhombus : A parallelogram with all sides equal in length is called a rhombus.
- Square : A parallelogram with all sides equal and each angle equal to 90° is called a square.
Area of a parallelogram
The area of a parallelogram is the region covered by it in a two-dimensional plane. The area of a parallelogram is calculated as the product of base and height of it.
Area of parallelogram = base x height
Perimeter of a parallelogram
The perimeter of a parallelogram is the total length of its boundary. As we know that, the parallelogram has equal opposite sides and if there are side lengths of parallelogram as a and b, then, the perimeter of a parallelogram, P = 2 (a + b).
Rapid Recall
In parallelogram
- Number of side = 4
- Number of vertices = 4
- Parallel sides = 2 pairs
- Area = base x height
- Perimeter = 2 (a + b)
Solved Parallelogram Examples
Example 1: Calculate the area of the given parallelogram.
Solution:
Area of parallelogram = base x height [Write the formula]
⇒ 8 x 5 [Substitute 8 for base and 5 for height]
⇒ 40
So, the area of the given parallelogram is 40 square inches.
Example 2: A garden is in the shape of a parallelogram as shown in the image. Find the length of fencing wire required to fence the boundary of this garden.
Solution :
Fencing is done on the boundary so we have to find the perimeter of the garden.
P = 2 (a + b) [Write the formula for perimeter of parallelogram]
P = 2 (80 + 100) [Substitute 80 for a and 100 for b]
P = 2 x 180 [Add]
P = 360 [Multiply]
So, 360 meters of fencing wire is needed to fence the boundary of the garden.
Example 3: Find the value of x.
Solution:
\(\angle\)ABC = \(\angle\)ADC [Opposite angles of parallelogram are equal]
x + 25 = 75 [Substitute x + 25 for \(\angle\)ABC and 75 for \(\angle\)ADC]
x + 25 – 25 = 75 – 25 [Subtract 25 from each side]
x = 50 [Subtract]
So, the value of x is 50.
A type of quadrilateral whose opposite sides are parallel and equal, is called a parallelogram.
A special parallelogram, known as a square is a polygon having equal sides and each angle measuring 90 degrees.
In a parallelogram the pairs of opposite sides are parallel. However, in trapezoids, exactly one pair of opposite sides is parallel.
There are three types of parallelograms and they are:
- Rectangle
- Rhombus
- Square
The adjacent angles of a parallelogram are supplementary angles.
When each side of a parallelogram is equal in length, then it is called a rhombus.