Calculating the area and perimeter of parallelograms can be very easy!

Here’s how you do it:

1. Perimeter is always = the Path around an object. In a parallelogram, just add up the lengths of all four sides.
2. The formula for the area of a parallelogram is A = b • h, where b is the base and h is the height.

Example:
1.) Find the perimeter and area of the following parallelogram:

PERIMETER:

All we need here are the length of the base (10 in) and the slant height (7.5 in).
Since a parallelogram has two sets of parallel sides, we know that opposite sides will be the same length.

To find the perimeter add 10 in + 7.5 in + 10 in + 7.5 in.
Perimeter = 35 in.

AREA:

The only numbers we need from our picture are the base (10 in) and the height (7 in).
A = b • h, so A = (10 in)(7 in) = 70 in²

Would you like to know why the formula for the area of a parallelogram is base times height?

In a parallelogram, we know that opposite sides are both parallel and congruent (the same length). Let’s take the parallelogram above and draw on the height.

Remember, the height is the imaginary line that cuts straight through the parallelogram, from the top to the bottom, at a right angle. Let’s actually cut off the little triangle we just made and move it from the left side of the parallelogram to the right.

Do you see what we’ve just done? We just turned our parallelogram into a rectangle! The base of the parallelogram is now the base of the rectangle and the height is exactly the same.
Since the area of a rectangle is base times height, the area of a parallelogram is too.