Question

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

Answer 1

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 * 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 = "opposite"/"hypotenuse" = h/a`

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

`h = sin (A) * a`

Your area is

`A = b * h = sin(A) * a * h`.

Hope that this helped!