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

1 Answer
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:

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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!