Pythagoras' Theorem - Short Problems

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

 

Out the Window

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

Weekly Problem 3 - 2012
Find out how many pieces of hardboard of differing sizes can fit through a rectangular window.

Folded Over

Stage: 3 Short Challenge Level: Challenge Level:1

Weekly Problem 11 - 2012
A rectangular piece of paper is folded. Can you work out one of the lengths in the diagram?

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?

Tetromino Diagonal

Stage: 3 Short Challenge Level: Challenge Level:1

Weekly Problem 10 - 2010
Can you calculate the length of this diagonal line?

Circle Time

Stage: 3 Short Challenge Level: Challenge Level:1

Weekly Problem 19 - 2010
Three circles of different radii each touch the other two. What can you deduce about the arc length between these points?

Centre Square

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

Weekly Problem 3 - 2011
What does Pythagoras' Theorem tell you about the radius of these circles?

Folding in Half

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

How does the perimeter change when we fold this isosceles triangle in half?

Unusual Polygon

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

Weekly Problem 20 - 2011
What is the perimeter of this unusually shaped polygon...

Indigo Interior

Stage: 3 Short Challenge Level: Challenge Level:1

Weekly Problem 5 - 2013
The diagram shows 8 shaded squares inside a circle. What is the shaded area?

Triangular Teaser

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

Weekly Problem 14 - 2014
Triangle T has sides of lengths 6, 5 and 5. Triangle U has sides of lengths 8, 5 and 5. What is the ratio of their areas?

One or Two

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

Weekly Problem 16 - 2014
The diagrams show squares placed inside semicircles. What is the ratio of the shaded areas?

Crane Arm

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

Weekly Problem 21 - 2014
A parallelogram is formed by joining together four equilateral triangles. What is the length of the longest diagonal?

Salt's Mill

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

Weekly Problem 49 - 2015
A window frame in Salt's Mill consists of two equal semicircles and a circle inside a large semicircle. What is the radius of the circle?

Right-angled Midpoints

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

Weekly Problem 33 - 2017
If the midpoints of the sides of a right angled triangle are joined, what is the perimeter of this new triangle?