### Square Areas

Can you work out the area of the inner square and give an explanation of how you did it?

### Dissect

What is the minimum number of squares a 13 by 13 square can be dissected into?

### 2001 Spatial Oddity

With one cut a piece of card 16 cm by 9 cm can be made into two pieces which can be rearranged to form a square 12 cm by 12 cm. Explain how this can be done.

# Square Coordinates

##### Age 11 to 14Challenge Level

Play with this interactivity until you can draw tilted squares confidently.

Formulate and describe a general instruction for the construction of a square when you are given two adjacent corners.

Formulate and describe a general instruction for the construction of a square when you are given two opposite corners.

Decide whether any of the collections of points below form a square.
If so, which ones?
Can you do this without plotting the points on a grid?

1. $(8,3)$, $(7,8)$, $(2,7)$, $(3,2)$
2. $(3,3)$, $(7,4)$, $(8,8)$, $(4,7)$
3. $(16,19)$, $(18,22)$, $(21,20)$, $(19,17)$
4. $(4,20)$, $(21,19)$, $(20,2)$, $(3,3)$

Explain how you decided.