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# Parallelogram Area Calculator

Parallelogram area formulasHow to use this parallelogram area calculator?FAQs

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.

• 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:

1. 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.

2. 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.

3. 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:

1. The length of adjacent sides and the angle between them – use trigonometry.
2. The length of diagonals and the angle between them, using the formula – use trigonometry.
3. 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.