Home / United States / Math Classes / Formulas / Area of Polygons: Parallelogram Formulas

A polygon is a closed figure in a two-dimensional plane. A polygon is also made up of three or more line segments known as the sides of the polygon. Triangles, squares, parallelograms, rhombuses, pentagons, hexagons, and so on, are a few examples of polygons. The area of a polygon is the measure of the space or region enclosed by the polygon. Each type of polygon has one or more formulas to calculate its area. Here we will focus on the formula used to calculate the area of a parallelogram....Read MoreRead Less

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.

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.

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.

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.

Frequently Asked Questions

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.