# Area of a Parallelogram Calculator

Area of a Parallelogram Calculator is a free online tool that assists students to calculate the area of a parallelogram easily. You can select any one of the three processes to find the parallelogram area. They are using base and height, using sides and angle between them, using diagonals and angle between them.

# Area of a Parallelogram Calculator (Base and Height)

**Here are some samples of Area of a Parallelogram calculations(Base and Height)**

# Area of a Parallelogram Calculator (Sides and Angle)

**Here are some samples of Area of a Parallelogram calculations(Sides and Angle)**

# Area of a Parallelogram Calculator (Diagonals and Angle)

**Here are some samples of Area of a Parallelogram calculations(Diagonals and Angle)**

### Formulas to Find Area of a Parallelogram

Three different formulas to check the parallelogram area are listed here

1. When you know base and height of parallelogram

Parallelogram area = b * h

Where, b is the base of a parallelogram

h is the height of a parallelogram

2. When you have two sides and angle of a parallelogram

Area of a parallelogram = a * b * sin(α)

Where, a, b are the lengths of sides of a parallelogram

α is the angle between two sides.

3. If you know parallelogram two diagonals, angle

Area = e * f * sin(α)

Where, e, f are the lengths of two diagonals of parallelogram

α is the angle between diagonals of parallelogram

Area of a Parallelogram Calculator

### Step by Step Process to Find Parallelogram Area

The following are the simple and easy steps to calculate the area of a parallelogram are given below.

**1. Using base and height**

- Check the side length and height of the parallelogram from the question.
- Perform the multiplication of those two parameters to get the answer.

**2. Sides Angle Between Them**

- Note down all the parameters about parallelogram in the given question.
- Multiply the length of sides of a parallelogram.
- Apply the sine function to the angle between the sides.
- Multiply the values obtained in the above steps to find the parallelogram area.

**3. Diagonals Angle Between Them**

- Take the length of two diagonals and angle between the diagonals.
- Perform the multiplication of diagonals length.
- Find the sin of angle between the diagonals.
- Multiply those values to get the accurate answer.

### Examples on Area of a Parallelogram

**Example 1: **The angle between any two sides of a parallelogram is 45 degrees. If the length of the two parallel sides is 3 cm and 4 cm respectively, then find the area?

**Solution: **

Given that,

Angle α = 45 degrees

a = 3 cm, b = 4 cm

Area of a parallelogram = a * b * sin(α)

By putting the given values in the formula.

area = 3 * 4 * sin(45°)

= 12 * (1/√2) = 8.485

∴ Area of a parallelogram is 8.485 cm².

**Example 2: **A parallelogram has sides 12 cm and 9 cm. If the distance between its shorter sides is 8 cm, find the distance between its longer side.

**Solution: **

Given that,

a = 12 cm, base = 9 cm

Height h = 8 cm

Area = b * h

= 8 * 9

= 72

∴ Area of a parallelogram is 72 cm².

**Example 3: **Find the area of a parallelogram with a diagonals 7 inches, 10 inches and angle is 60 degrees.

**Solution: **

Given that,

Angle α = 60 degrees

e = 7 inches, f = 10 inches

parallelogram area = e * f * sin(α)

= 7 * 10 * sin(60°)

= 70 * (√3/2)

= 60.621

∴ Area of a parallelogram is 60.621 sq units.

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### Frequently Asked Questions on Parallelogram Area

**1. What is Meant by Area of a Parallelogram?**

Parallelogram is a type of quadrilateral having 2 pairs of parallel sides of equal length and two diagonals. The region occupied by the parallelogram with the given dimensions is the area of a parallelogram.

**2. How do you find the parallelogram area using calculator?**

Students have to enter input in the fields, also select the units from the beside field and tap on the calculate button which in blue color to obtain the parallelogram area in fraction of seconds.

**3. What is the formula to calculate area of a parallelogram with diagonals?**

The formula to find the parallelogram using diagonals length is here.

Area = diagonal1 * diagonal2 * sin(angle).

**4. How do you find the area of a parallelogram with only sides?**

Parallelogram area = a * b * sin(θ). Where a, b are the length of sides of parallelogram and θ is the angle between sides.