# Completing Quadrilaterals

##### Age 11 to 14

Challenge Level

Special Cases

How do you define a rectangle? There are lots of possible definitions, such as:

**A quadrilateral with four right angles.**

Does a square satisfy this definition?

Answer: yes!

This means that a square is a special type of rectangle: it meets all of the criteria for a rectangle but has other special properties. Take a look at these rectangles:

One of these is special, and is given the extra name of a square, but it is still a rectangle. It is a **special case** of a rectangle.

*Notice that all squares are rectangles, but not all rectangles are squares. Think about the right-hand rectangle above.*

Here are some other examples of special cases:

These are a collection of rhombuses, one of which is also a square.

These are a collection of kites, one of which is also a rhombus.

This is a collection of parallelograms, one of which is also a rectangle.

**Two standard methods for working out the areas of tilted squares, which may help to work out the areas of the quadrilaterals:**

Splitting the tilted square into right-angled triangles and squares and adding the areas of the different parts:

Boxing in the square, working out the area of the box and subtracting the areas of the unwanted right-angled triangles: