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Grid Lockout
Age 14 to 16
Challenge Level 
Investigate the areas of squares formed by joining points on a square grid and show that it is impossible to construct any square whose area is (4n + 3) where n is an integer.
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Some(?) of the Parts
A circle touches the lines OA, OB and AB where OA and OB are perpendicular. Show that the diameter of the circle is equal to the perimeter of the triangle
Ladder and Cube
A 1 metre cube has one face on the ground and one face against a wall. A 4 metre ladder leans against the wall and just touches the cube. How high is the top of the ladder above the ground?
At a Glance
The area of a regular pentagon looks about twice as a big as the pentangle star drawn within it. Is it?