2D shapes and their properties

Use the isometric grid paper to find the different polygons.

How can these shapes be cut in half to make two shapes the same shape and size? Can you find more than one way to do it?

How many trapeziums, of various sizes, are hidden in this picture?

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

The image in this problem is part of a piece of equipment found in the playground of a school. How would you describe it to someone over the phone?

Bluey-green, white and transparent squares with a few odd bits of shapes around the perimeter. But, how many squares are there of each type in the complete circle? Study the picture and make an estimate.

What is the ratio of the area of a square inscribed in a semicircle to the area of the square inscribed in the entire circle?

Can you find a relationship between the area of the crescents and the area of the triangle?

By inscribing a circle in a square and then a square in a circle find an approximation to pi. By using a hexagon, can you improve on the approximation?

Identical squares of side one unit contain some circles shaded blue. In which of the four examples is the shaded area greatest?