You may also like

problem icon

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?

problem icon

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.

problem icon

Lap Times

Two cyclists, practising on a track, pass each other at the starting line and go at constant speeds... Can you find lap times that are such that the cyclists will meet exactly half way round the track.

Doesn't Add Up

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

The square below has side length 8 and area 64, but the area of the rectangle is 65 (13 by 5). 

It seems that the same four pieces can make two shapes with different areas!

Can you explain where the extra area comes from?

(You might like to try cutting out the shapes from a piece of paper.)

Here are some questions you might like to consider:

Can other squares be split up and rearranged to make rectangles with a different area?

Are there other square/rectangle pairs where the areas differ by 1 square unit?

Is there a pattern in the sizes of squares that can be arranged in this way?