how to find the height of a parallelogram

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 is working - 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's not working the other way round!

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 rectangle area! 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 an angle between them

area = a * b * sin(angle)

Does it ring a bell? This formula comes from trigonometry, and is used for example in triangle area - 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 an angle between them

area = 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, 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: e * (f/2) * sin(angle)

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

How to find the area of a parallelogram?

You are still not sure how to use the parallelogram area calculator? 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 diagonals of a parallelogram and the angle between diagonals.
Enter the given values to the right boxes. Assume 5 in, 13 in and 30° for the first diagonal, 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, circle and trapezoid area calculator.