Squares

What fraction of this square is shaded?

Can you use the given image to say something about the sum of an infinite series?

How many tiles could you use to cover this 10 by 10 patio?

This activity investigates how you might make squares and pentominoes from Polydron.

Investigate all the different squares you can make on this 5 by 5 grid by making your starting side go from the bottom left hand point. Can you find out the areas of all these squares?

Cut off three right angled isosceles triangles to produce a pentagon. With two lines, cut the pentagon into three parts which can be rearranged into another square.

Given that ABCD is a square, M is the mid point of AD and CP is perpendicular to MB with P on MB, prove DP = DC.

Investigate how this pattern of squares continues. You could measure lengths, areas and angles.

If you continue the pattern, can you predict what each of the following areas will be? Try to explain your prediction.