# How do you find the area of a parallelogram with two sides and an angle?

Nov 25, 2015

So, let's assume that you have two different sides of the parallelogram so that the computations can work. :-)

Let's say that you have the sides $a$ and $b$ and the angle $A$ as in my drawing:

To determine the area of the parallelogramm, you need the value of $h$ so that you can compute $A = b \cdot h$.

However, the height and the side $a$ are both parts of a right angle triangle, with $h$ being the opposite leg of the angle $A$ and $a$ being the hypotenuse of the triangle.

So, here, you can use the $\sin$ formula:

$\sin A = \text{opposite"/"hypotenuse} = \frac{h}{a}$

This means that you can compute $h$ like this:

$h = \sin \left(A\right) \cdot a$

$A = b \cdot h = \sin \left(A\right) \cdot a \cdot h$.