A red square and a blue square overlap so that the corner of the red square rests on the centre of the blue square. Show that, whatever the orientation of the red square, it covers a quarter of the. . . .
A tennis ball is served from directly above the baseline (assume the ball travels in a straight line). What is the minimum height that the ball can be hit at to ensure it lands in the service area?
If the sides of the triangle in the diagram are 3, 4 and 5, what is the area of the shaded square?
Draw all the possible distinct triangles on a 4 x 4 dotty grid. Convince me that you have all possible triangles.
Explain how the thirteen pieces making up the regular hexagon shown in the diagram can be re-assembled to form three smaller regular hexagons congruent to each other.
The triangles in these sets are similar - can you work out the lengths of the sides which have question marks?
How many rectangles can you find in this shape? Which ones are differently sized and which are 'similar'?
Construct two equilateral triangles on a straight line. There are two lengths that look the same - can you prove it?
Make your own pinhole camera for safe observation of the sun, and find out how it works.