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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?

From All Corners

Straight lines are drawn from each corner of a square to the mid points of the opposite sides. Express the area of the octagon that is formed at the centre as a fraction of the area of the square.

Mediant Madness

Kyle and his teacher disagree about his test score - who is right?

Doesn't Add Up

Age 14 to 16
Challenge Level

Two prompts :
  • Cut an 8 by 8 square into the four pieces and rearrange them as shown
  • What is the area of each piece ?