Two Squared

What happens to the area of a square if you double the length of the sides? Try the same thing with rectangles, diamonds and other shapes. How do the four smaller ones fit into the larger one?
Exploring and noticing Working systematically Conjecturing and generalising Visualising and representing Reasoning, convincing and proving
Being curious Being resourceful Being resilient Being collaborative


If you double the sides of a square, the area becomes four times the size. It is quadrupled.

Image
Two Squared



We can try the same thing with a rectangle and a rhombus.

How do the four smaller ones fit into the larger one?

Image
Two Squared

#set var="roll-text" value="Be a detective!" #set var="roll-text" value=""



We can then try with equilateral triangles:

Image
Two Squared


And "L" shapes:

Image
Two Squared


What has to be done to make these fit?

#set var="roll-text" value="Be a detective!" #set var="roll-text" value=""

We could try with other shapes like hexagons.

These have to be cut and rearranged.

Image
Two Squared


What is the least number of cuts needed to fit four hexagons into one larger hexagon with sides double the length?

#set var="roll-text" value="Be a detective!" #set var="roll-text" value=""