Quadrilaterals

Doors, screens, fields, tiles: a great deal of what you see around you has four corners. Quadrilaterals are so handy because they fit together without gaps and because you get their area with a short calculation. Here you learn to tell the four most important quadrilaterals apart and to work out their areas.

What all quadrilaterals share

A quadrilateral always has four sides and four corners. And just as with the triangle there is a fixed angle rule: the four interior angles add up to 360°. In the square and the rectangle each of these angles is a right angle of 90°, which fits the rule exactly: $4 \cdot 90° = 360°$.

Square and rectangle

A rectangle has four right angles, and opposite sides are equally long. Its area is length times width. The square is a special rectangle in which all four sides are equally long. So its area is simply side times side, that is, the side squared.

The parallelogram

A parallelogram looks like a tilted rectangle: opposite sides are parallel and equally long, but there are usually no right angles at its corners. If all four are right angles, you are looking at a rectangle, because a rectangle is simply a parallelogram without the tilt. For the area what counts is not the slanted side but the height. That is the perpendicular distance between the base and the opposite side. The base is just the side the shape stands on. The area is base times height.

The trapezoid

A trapezoid has two parallel sides that may differ in length, $c$ at the top and $a$ at the bottom. For the area you take the average of the two parallel sides and multiply it by the height. With $a = 8$, $c = 4$ and height $h = 5$ this gives $\frac{8 + 4}{2} \cdot 5 = 6 \cdot 5 = 30$.