So, if you’ve not yet had a giggle today, here’s a good one: What sort of public transportation do parallelograms like to use? Are you ready for this? The rhom-BUS! Get it? Snicker, snicker, groan…. OK, well, there is a relationship, in case you didn’t know. There is a relationship between all closed coplanar figures made from line segments.

Geometric shapes are a lot like those Russian matryoshka dolls that nest one inside the other. You open one to find another, and open that one to find yet another. The difference between dolls and geometry figures is that geometry figures are a bit more … shall we say, angular? Each successive doll is a miniature of the one in which it nested, whereas geometric figures don’t all look the same. Still, they nest as regards definition.

Take the parallelogram, for example. What is a parallelogram? A parallelogram is a quadrilateral in which both pairs of sides are parallel to one another. Well, if a parallelogram is a quadrilateral, then what is that? The word quadrilateral means four sides. A quadrilateral is a four-sided polygon.

OK, well then, what is a polygon? A polygon is any one of many coplanar line segments (what most folks think of as two-dimensional, or flat) where each line segment is connected end to end to another to form a closed shape.

So, if you open the doll labeled polygon, you might find inside a quadrilateral. Open the quadrilateral, and one of the shapes that might pop out is a parallelogram. That’s where the fun starts, because the parallelogram gives birth to rectangles, squares and the zooming rhombus. Really!

See, a rectangle is a special kind of parallelogram in which not only are both pairs of its sides parallel, but all the shape’s interior angles are 90°.

A rhombus is a parallelogram with all four sides equal in length.

And then we have the humble square, which is both a rhombus and a parallelogram. Its pairs of sides are parallel, its sides are of equal length and all of its interior angles are 90°.

There are various formulas that calculate the area of these shapes. The formula for the area of a parallelogram is also the formula to find the area of the rectangle, the rhombus and the square, because they are all, in essence, parallelograms.

A = B x H where A = area, B = the base and H = the height.

Determining the base of a parallelogram is easy! Simply pick a side! With a parallelogram, the formula works no matter which side one chooses as the base. It can be the long side, the short side, and of course, with the square and the rhombus, the side lengths are equal. All it takes to master parallelograms is the ability to think outside the box!