Pythagoras's - Short Problems

A collection of short Stage 3 and 4 problems on Pythagoras's Theorem

 

Weekly Problem 3 - 2012

Stage: 3 Challenge Level: Challenge Level:1

Find out how many pieces of hardboard of differing sizes can fit through a rectangular window.

Weekly Problem 36 - 2007

Stage: 3 and 4 Challenge Level: Challenge Level:1

Find the length along the shortest path passing through certain points on the cube.

Weekly Problem 2 - 2008

Stage: 3 and 4 Challenge Level: Challenge Level:2 Challenge Level:2

The diagram shows two semicircular arcs... What is the diameter of the shaded region?

Weekly Problem 5 - 2008

Stage: 3 and 4 Challenge Level: Challenge Level:1

Calculate the ratio of areas of these squares which are inscribed inside a semi-circle and a circle.

Weekly Problem 24 - 2008

Stage: 3 and 4 Challenge Level: Challenge Level:1

The diagram shows two circles and four equal semi-circular arcs. The area of the inner shaded circle is 1. What is the area of the outer circle?

Weekly Problem 40 - 2009

Stage: 3 Short Challenge Level: Challenge Level:1

This quadrilateral has an unusual shape. Are you able to find its area?

Weekly Problem 10 - 2010

Stage: 3 Short Challenge Level: Challenge Level:1

Try to calculate the length of this diagonal line. Are you able to find more than one method?

Weekly Problem 19 - 2010

Stage: 3 Short Challenge Level: Challenge Level:1

Three circles of different radii each touch the other two. What can you deduce about the arc length between these points?

Weekly Problem 3 - 2011

Stage: 3 and 4 Short Challenge Level: Challenge Level:1

What does Pythagoras' Theorem tell you about the radius of these circles?

Weekly Problem 20 - 2011

Stage: 2 and 3 Short Challenge Level: Challenge Level:1

What is the perimeter of this unusually shaped polygon...

Weekly Problem 14 - 2014

Stage: 3 and 4 Challenge Level: Challenge Level:1

Weekly Problem 14 - 2014

Weekly Problem 16 - 2014

Stage: 3 and 4 Challenge Level: Challenge Level:2 Challenge Level:2

Weekly Problem 16 - 2014

Weekly Problem 21 - 2014

Stage: 3 and 4 Challenge Level: Challenge Level:1

Weekly Problem 21 - 2014