Parallelogram Area Calculator

Area is a numerical characteristic of a two-dimensional (flat or curved) geometric figure, informally speaking, showing the size of this figure. Historically, the calculation of the area was called quadrature. A figure having an area is called quadratic. Find the area of more than 22 shapes (triangle, square, pentagon, etc.) using our amazing calculator.

Parallelogram — is a quadrangle in which the opposite sides are pairwise parallel, that is, they lie on parallel lines. Particular cases of a parallelogram are a rectangle, a square, and a rhombus.

A parallelogram is a four-sided polygon with two pairs of parallel sides. To calculate the area of a parallelogram, you need to know the length of the base and the height. Our calculator makes it easy to find the area of your parallelogram using different methods:

• Diagonals and the angle between them
• Sides and the angle between them
• Side and height

Parallelogram Area Formulas

There are three main formulas to find the area of a parallelogram:

• Diagonal and Angle Formula: A = (d₁ × d₂ × sin(θ)) / 2. This formula is used when you know the length of the two diagonals and the angle between them. The formula is derived from the fact that the area of a parallelogram is equal to half the product of its diagonals multiplied by the sine of the angle between them.
• Side and Angle Formula: A = a × b × sin(θ). This formula is used when you know the length of two adjacent sides and the angle between them. The formula is derived from the fact that the area of a parallelogram is equal to the product of its adjacent sides multiplied by the sine of the angle between them.
• Side and Height Formula: A = b × h. This formula is used when you know the length of one side and the height of the parallelogram. The formula is derived from the fact that the area of a parallelogram is equal to the product of its base and height.

How to Use the Parallelogram Area Calculator

To use our parallelogram area calculator:

1. Select the method you want to use to find the area of your parallelogram.
2. Enter the required values in the input boxes.
3. Our calculator automatically will give you the answer.

Example

Let's say you have a parallelogram with diagonals of length 8 cm and 10 cm, and an angle between them of 45 degrees. To find the area using the diagonal and angle formula:

1. Select the `Diagonal and Angle` method in the calculator.
2. Enter 8 cm and 10 cm in the input boxes for the diagonal lengths.
3. Enter 45 degrees in the input box for the angle.
4. Our calculator automatically will give you the answer.

The area of the parallelogram will be (8 cm × 10 cm × sin(45°)) / 2 = 28.28 square centimeters.

Conclusion

Calculating the area of a parallelogram can be a tricky task. Our parallelogram area calculator and formulas make it easy to find the area of your parallelogram using different methods.