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?

Walk the Plank

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

Weekly Problem 22 - 2006
A rectangular plank fits neatly inside a square frame when placed diagonally. What is the length of the plank?

Right Angled Possibilities

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

Weekly Problem 23 - 2007
If two of the sides of a right-angled triangle are 5cm and 6cm long, how many possibilities are there for the length of the third side?

Common Tangent

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

Weekly Problem 33 - 2007
Two circles touch, what is the length of the line that is a tangent to both circles?

Hamiltonian Cube

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

Weekly Problem 36 - 2007
Find the length along the shortest path passing through certain points on the cube.

Rectriangle

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

Weekly Problem 48 - 2007
A 3x8 rectangle is cut into two pieces... then rearranged to form a right-angled triangle. What is the perimeter of the triangle formed?

Semicircle in a Semicircle

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

Weekly Problem 2 - 2008
The diagram shows two semicircular arcs... What is the diameter of the shaded region?

Interior Squares

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

Weekly Problem 5 - 2008
Calculate the ratio of areas of these squares which are inscribed inside a semi-circle and a circle.

Oh So Circular

Stage: 4 Short Challenge Level: Challenge Level:1

Weekly Problem 24 - 2008
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?

Unusual Quadrilateral

Stage: 3 Short Challenge Level: Challenge Level:1

Weekly Problem 40 - 2009
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?