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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?

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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.

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Lap Times

Can you find the lap times of the two cyclists travelling at constant speeds?

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 ?