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# Parallelogram Formula

A parallelogram is a two-dimensional shape. It has four sides, in which two pairs of opposite sides are parallel. The opposite sides of a parallelogram are equal in length, and the opposite angles are equal in measure, while the sum of adjacent angles of a parallelogram is equal to 180 degrees. Before moving into the parallelogram formula let's have a look into its properties.

### Properties of a Parallelogram

Few important properties of a parallelogram are listed below:

- The opposite sides are parallel and congruent.
- The interior opposite angles are congruent.
- The consecutive angles are supplementary.
- In case, if the measure of any one of the angles is a right angle, then all the other angles will be the right angle.
- The two diagonals bisect each other.
- Each diagonal bisects the parallelogram into two congruent triangles
- The sum of squares of all the sides of a parallelogram is equal to the sum of the square of its diagonals which is known as the parallelogram law.

## What Is Parallelogram Formula?

Consider parallelogram ABCD as shown below. Let's understand the Parallelogram Formulas.

We have,

- AB || CD, AC || BD
- AB = CD = b
- BC = AD = a
- h = height of the parallelogram
- DB = d\(_1\), AC = d\(_2\) are digonals of the parallelogram

### Area of a Parallelogram Formula

The area of a parallelogram is the region or surface occupied by a two-dimensional plane. Let's look into the parallelogram formula to calculate area.

**Area of Parallelogram Formula Using Base and Height**

- Area of parallelogram formula = Base × Height
- Area of parallelogram ABCD = b × h

**Area of a Parallelogram Formula Without Height**

- If the height of the parallelogram is not given, trigonometry can be used to find the area.
- Area of parallelogram formula = a b sin A = b a sin B

**Area of a Parallelogram Using Diagonals**

The area of any parallelogram can also be calculated using its diagonal lengths. Suppose, the diagonals d\(_1\) and d\(_2\) intersect each other at an angle x, then the area of the parallelogram is given by:

- Area of parallelogram formula = ½ ×\({d_1} × {d_1} sin (x)\)
- Area of parallelogram ABCD = ½ × AC × BD sin (x)

### Perimeter of a Parallelogram Formula

The perimeter of a parallelogram is the total distance of the boundaries of the parallelogram. To calculate the perimeter of a parallelogram, its length and breadth have to be known. Let the sides of the parallelogram be a and b. Keeping the property of a parallelogram in mind, i.e., the opposite sides are parallel and congruent. The perimeter of a parallelogram is given by:

- Perimeter = a + b + c + d (when a, b, c, d are representing 4 sides of a parallelogram)
- Since, side AB = CD = b, side BC = AD = a
- Perimeter of a parallelogram = 2 (a+b)

## Example on Parallelogram Formula

**Example 1:** Using the parallelogram formula, find the area of the parallelogram with the base of 6 cm and height of 8 cm.

**Solution:**

Given:

Base, b = 6 cm

Height, h = 8 cm

We know that, using parallelogram formula

Area of Parallelogram formula = b × h square units

= 6 × 8 = 48 sq.cm

**Answer: Therefore, the area of the parallelogram = 48 cm ^{2}.**

**Example 2:** Using the parallelogram formula, find the perimeter of a parallelogram with side measures 5 m and 7 m.

**Solution:**

Given:

a = 5 m

b = 7 m

We know that,

Perimeter of a Parallelogram = 2( a + b) units

= 2(5 + 7)

= 24 m

**Answer: Thus, the perimeter of the parallelogram is 24 m.**

**Example 3: **The area of a playground that is in the shape of a parallelogram is 25000 in^{2}, with one side measuring 250 in. Find the corresponding altitude using the area of the parallelogram formula.

**Solution:**

Area of the playground = 25000 in^{2}

Side of a playground = 250 in

Using Area of Parallelogram formula = b × h square units

Corresponding altitude = 25000/250 = 100 in

**Answer:** Corresponding altitude of the playground measures 100 inches.

## FAQs on Parallelogram Formula

### How Do You Calculate Area Using Parallelogram Formula?

If the base and the height (altitude) of a parallelogram are given, then the area can be expressed as the product of the base and the height of the parallelogram.

A = bh

A = Base × Height (units^{2})

### What Is the Parallelogram Formula To Calculate the Perimeter?

To calculate the perimeter of a parallelogram we use the general parallelogram formula mentioned below:

Perimeter of a parallelogram = 2 (a+b) units

### What Is 'h' in Parallelogram Formula for Area?

The area of the parallelogram formula is given as, A = bh square units. Here 'h' represents the height (altitude) of a parallelogram.

### What Is 'B' in Parallelogram Formula for Area?

The area of the parallelogram formula is given as, A = B × H square units. Here 'B' represents the base of a parallelogram.

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