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?
Can you work out the dimensions of the three cubes?
A square of area 40 square cms is inscribed in a semicircle. Find
the area of the square that could be inscribed in a circle of the
The area of a square inscribed in a circle with a unit radius is, satisfyingly, 2. What is the area of a regular hexagon inscribed in a circle with a unit radius?
It's easy to work out the areas of most squares that we meet, but
what if they were tilted?
A spider is sitting in the middle of one of the smallest walls in a
room and a fly is resting beside the window. What is the shortest
distance the spider would have to crawl to catch the fly?
Chris is enjoying a swim but needs to get back for lunch. If she can swim at 3 m/s and run at 7m/sec, how far along the bank should she land in order to get back as quickly as possible?
Can you make sense of these three proofs of Pythagoras' Theorem?
Can you minimise the amount of wood needed to build the roof of my garden shed?
A collection of short Stage 3 and 4 problems on Pythagoras's Theorem.
A vine is growing up a pole. Can you find its length?
A palm tree has snapped in a storm. What is the height of the piece that is still standing?
A circle of radius 1 is inscribed in a regular hexagon. What is the perimeter of the hexagon?
Can you find the distance from the well to the fourth corner, given the distance from the well to the first three corners?
When you pull a boat in using a rope, does the boat move more quickly, more slowly, or at the same speed as you?