What is a Parallelogram?
A parallelogram has four sides, and the pairs of opposite sides are parallel. In a parallelogram, the opposite sides are also equal in length and the opposite angles are equal in measure.
A rectangle and a parallelogram are similar quadrilaterals. Hence, the area of a parallelogram can be determined in the same way as the area of a rectangle.
The area of a Parallelogram Formula
We can use the following formula to calculate the area of a parallelogram:
Area of parallelogram, A = bh
We will discuss this formula in detail in the next section.
How do we use the area of a Parallelogram Formula?
To calculate the area of a parallelogram, you need the measure of its base and height.
As we just saw, the area of a parallelogram is the product of its base and height. The area is measured in square units.
Mathematically, the area of a parallelogram can be expressed as:
Area of parallelogram = bh
Where,
- b = base of the parallelogram
- h = height of the parallelogram
Note:
- The base and the height are perpendicular to each other.
- The lateral side is not perpendicular to the base.
- The base of a parallelogram can be either the horizontal or the vertical side.
Solved Examples
Example 1: Find the area of the given parallelogram.
Solution:
A = bh [Formula for the area of a parallelogram]
= 10 x 8 [Substitute the given values]
= 80 [Multiply]
Example 2:
Calculate the area of a parallelogram with a base of 7 inches and a height of 18 inches.
Solution:
A = bh [Formula for the area of a parallelogram]
= 7 x 18 [Substitute the given values]
= 126 [Multiply]
Hence, the area of the parallelogram is 186 square inches.
Hence, the area of the given parallelogram is 80 square units.
A = bh [Formula for the area of a parallelogram]
= 10 x 8 [Substitute the given values]
= 80 [Multiply]
Hence, the area of the given parallelogram is 80 square units.
Example 3:
Calculate the height of the parallelogram given in the figure.
Solution:
A = bh [Formula for the area of a parallelogram]
24 = 4 x h [Substitute the given values]
\(\frac{24}{4}=\frac{4~\times~h}{4}\) [Divide by 4 on both sides]
6 = h [Simplify]
Or
h = 6
Hence, the height of the parallelogram is 6 cm.
Example 4:
Calculate the base of the parallelogram given in the figure.
Solution:
A = bh [Formula for the area of a parallelogram]
20 = b x 4 [Substitute the given values]
\(\frac{20}{4}=\frac{b~\times~4}{4}\) [Divide by 4 on both sides]
5 = b [Simplify]
Or
b = 5
Hence, the base of the parallelogram is 5 m.
Example 5:
The area of a parallelogram-shaped side of a building is 900 square yards. Calculate the altitude of the building.
Solution:
The altitude of the building is the height “h” of the building.
From the figure, the base of the parallelogram-shaped building measures 60 yards.
A = bh [Formula for the area of a parallelogram]
900 = 60 x h [Substitute the given values]
\(\frac{900}{60}=\frac{60~\times~h}{60}\) [Divide by 60 on both sides]
15 = h [Simplify]
Or
h = 15
Hence, the height of the parallelogram-shaped building is 15 yards.
The perimeter of a parallelogram is the sum of the measures of all its sides.
A parallelogram does not have a line of symmetry. Neither does it have a horizontal line of symmetry nor will a vertical line of symmetry divide a parallelogram into two halves.
The different types of parallelograms are:
- Squares
- Rectangles
- Rhombuses
The area of a parallelogram and a rectangle with a common base and between the same set of parallel sides have equal areas.
This is based on the fact that every parallelogram can be transformed into a rectangle.
The first figure is a parallelogram that has been transformed into a rectangle in the fourth figure. We can see that they both have the same area, that is, A = bh.
A quadrilateral is a type of polygon that has four sides. parallelograms, squares, rectangles, trapeziums, kites, and rhombuses, are examples of quadrilaterals.