Ratio and proportion

If the sides of the triangle in the diagram are 3, 4 and 5, what is the area of the shaded square?

Two motorboats travelling up and down a lake at constant speeds leave opposite ends A and B at the same instant, passing each other, for the first time 600 metres from A, and on their return, 400 metres from B. How long is the lake?

A trapezium is divided into four triangles by its diagonals. Can you work out the area of the trapezium?

Find the ratio of the outer shaded area to the inner area for a six pointed star and an eight pointed star.

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.

Which is a better fit, a square peg in a round hole or a round peg in a square hole?

If it takes four men one day to build a wall, how long does it take 60,000 men to build a similar wall?

One night two candles were lit. Can you work out how long each candle was originally?

Four jewellers share their stock. Can you work out the relative values of their gems?