Parallelogram Area Calculator

Q: How do I find the area of a parallelogram given its adjacent sides?

To determine the area given the adjacent sides of a parallelogram, you also need to know the angle between the sides . Then you can apply the formula: area = a × b × sin(α) , where a and b are the sides, and α is the angle between them.

Q: What is the area of a parallelogram with perpendicular diagonals of length 10 and 15?

The answer is 75 . We use the formula that says the area is equal to ½ times the product of the lengths of the diagonals times the sine of the angle between them. As our diagonals are perpendicular, the angle between them is 90° and sin 90° = 1 . Hence, the calculation we need to perform is ½ × 10 × 15 = 75 .

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Hanna Pamuła, PhD

Hanna PamułaPhD

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Hanna (Hania) Pamuła holds a Ph.D. in Bioacoustics / Mechanical Engineering, obtained at AGH University of Science and Technology. She has participated in research work in labs in France and the UK and presented papers at several international conferences. Hania has a penchant for photography and graphic design. When not in the office, she’s probably traveling, hiking, or out in the field, watching birds and recording their calls. See full profile

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Bogna Szyk

Bogna is the chief operating officer at Omni Calculator, where she helps keep things running smoothly and ideas moving forward. With a background in civil engineering and a knack for organizing chaos, she brings structure and strategy to everything she does. After hours, you’ll likely find her dancing zouk or crafting the next twist in a D&D campaign. See full profile

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and Steven Wooding

Steven Wooding

Steven Wooding is a physicist by training with a degree from the University of Surrey specializing in nuclear physics. He loves data analysis and computer programming. He has worked on exciting projects such as environmentally aware radar, using genetic algorithms to tune radar, and building the UK vaccine queue calculator. Steve is now the Editorial Quality Assurance Coordinator here at Omni Calculator, making sure every calculator meets the standards our users expect. In his spare time, he enjoys cycling, photography, wildlife watching, and long walks. See full profile

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If you have any problems with the geometry of a parallelogram, check this parallelogram area calculator (and also its twin brother, parallelogram perimeter calculator).

Whether you want to calculate the area given base and height, sides and angle, or diagonals of a parallelogram and angle between them, you are in the right place. Don't ask how to find the area of a parallelogram; just give the calculator a try!

Below you can find out how the tool works – the parallelogram area formulas and neat explanation are all you need to understand the topic.

Parallelogram area formulas

A parallelogram is a simple quadrilateral with two pairs of parallel sides. Every rectangle is a parallelogram, as well as every rhombus and square. Remember, it doesn't work the other way around!

Which formulas does the parallelogram area calculator use?

Area given base and height

area = base × height

Did you notice something? The formula for the area of a parallelogram is pretty much the same as for a rectangle! Why is it so? Have a look at the picture: a parallelogram can be divided into a trapezoid and a right triangle and rearranged to the rectangle.

Learn more about rectangle area with our area of a rectangle calculator.
Area given sides and the angle between them

area = a × b × sin(angle)

Does it ring a bell? This formula comes from trigonometry and is used, for example, in our triangle area calculator – the parallelogram may be seen as two congruent triangles. The adjacent angles in the parallelogram are supplementary, so you can choose whichever angle you want because sin(angle) = sin(180° - angle).
Area given diagonals of a parallelogram and the angle between them

area = ½ × e × f × sin(angle)

The formula comes from trigonometry as well. Do you want to know where it comes from?

Divide the parallelogram into two triangles, and assume that our e diagonal is the "base" for both new triangles.

What's the height of that triangle? Use the sine function. It's (f/2) × sin(angle)!

The area of the triangle is equal to our "base" e times height and divided by 2: e × (f/4) × sin(angle)

The parallelogram consists of two such triangles, so the area equals e × (f/2) × sin(angle).

How to use this parallelogram area calculator?

Are you still not sure our parallelogram area calculator works? We will show you step by step:

Have a look at your exercise. What is given, what is unknown? Choose the right calculator part for your needs. Assume that we want to calculate the area knowing the sides of a parallelogram and the angle between them.
Enter the given values to the right boxes. Assume 5 in, 13 in, and 30° for the first side, the second one, and the angle between them, respectively.
The calculator displays the area of a parallelogram value. It's 32.5 in² in our case.

Check out our area calculators for other shapes, such as rhombus area calculator, circle area calculator, and trapezoid area calculator.

FAQs

How do I find the area of a parallelogram given its adjacent sides?

To determine the area given the adjacent sides of a parallelogram, you also need to know the angle between the sides. Then you can apply the formula: area = a × b × sin(α), where a and b are the sides, and α is the angle between them.

How do I find the area of a parallelogram given diagonals?

The area of a parallelogram can be determined from its diagonals, provided that you also know the angle between the diagonals.

If e and f are the lengths of the diagonals and φ is the angle between them, then the area can be calculated as follows: area = ½ × e × f × sin(φ).

How do I find the area of a parallelogram without height?

It is possible to find the area of a parallelogram without height! For instance, it suffices to know one of the following things:

The length of adjacent sides and the angle between them – use trigonometry.
The length of diagonals and the angle between them, using the formula – use trigonometry.
The length of diagonals and one side – use Heron's formula.

What is the area of a parallelogram with perpendicular diagonals of length 10 and 15?

The answer is 75. We use the formula that says the area is equal to ½ times the product of the lengths of the diagonals times the sine of the angle between them. As our diagonals are perpendicular, the angle between them is 90° and sin 90° = 1. Hence, the calculation we need to perform is ½ × 10 × 15 = 75.