Parallelogram Area Calculator

Table of contents:
Do you want to calculate the area of a parallelogram when given the sides and angle? Or how about when you know the base and height? Perhaps you have the parallelogram’s diagonals and the angle between them, and that’s how you want to work out the area? Well if you answered ‘yes’ to any of those three questions, you have landed in the right place. Our calculator is the ideal solution for any issues you may have with a parallelogram’s geometry. Read on for information about the parallelogram formulas, and also a step-by-step explanation on how to use the calculator.

A look at the parallelogram area formulas

Before breaking down the formulas, it’s important to understand the function of a parallelogram. Well it is a basic quadrilateral which features a couple of pairs of parallel sides. Along with every rectangle being a parallelogram, so is every square and rhombus in existence. Now that is out of the way, let’s look at the parallelogram area calculator’s formulas: 

Area when given the sides and angle

area = a * b * sin(angle)

If you’ve completed high school math, you will likely recognize the above formula from trigonometry. This is because it is used, for example, when working out the triangle area. Well the parallelogram can be viewed as two corresponding triangles. As the parallelogram’s adjacent angles are supplementary, you can choose whatever angle for the formula because sin(angle) = sin(180° - angle).

Area when given the base and height

area = base * height

When working out the area with the base and height, you’ll see that it’s pretty much identical to the formula for solving a rectangle’s area. The reason behind this is you can divide a parallelogram into a trapezoid and right angle, and these shapes can be reorganized into a rectangle.

Area when given a parallelogram’s diagonals and an angle in between

area = e * f * sin(angle)

This is another formula that is found from the world of trigonometry. However, this one’s a little trickier than the aforementioned methods.
To get a better understanding, first take the parallelogram and divide it into two triangles. Now consider the ‘base’ for both triangles to be the e diagonal. Yet when finding out the area of a triangle, you need to times the ‘base’ (e) with its height (f/2) * sin(angle). That equation being: e * (f/2) * sin(angle).
Yet this isn’t the end! Don’t forget that the parallelogram is made up of two triangles, so the area formula is: e * f * sin(angle).

Finding the parallelogram’s area

If you are still finding it tricky to utilize our parallelogram calculator, here’s a step-by-step guide:

1.	To begin with, you need to know which calculator matches your needs. For this example, we’ll go with the calculator that solves the parallelogram’s area when given the base and height. 
2.	Enter the right values in the right sections. In this case, we’ll say the base and height are 30cm and 20cm respectively.
3.	The calculator will now display the area of the parallelogram, which is 600cm². It’s that easy!

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