Geometrical Reasoning - Short Problems

A collection of short Stage 4 problems on geometrical reasoning



Weekly Problem 4 - 2008

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

In the figure given in the problem, calculate the length of an edge.

Weekly Problem 23 - 2008

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

A triangle has been drawn inside this circle. Can you find the length of the chord it forms?

Weekly Problem 34 - 2008

Stage: 3 Short Challenge Level: Challenge Level:2 Challenge Level:2

What is the area of the region common to this triangle and square?

Weekly Problem 27 - 2009

Stage: 3 Short Challenge Level: Challenge Level:2 Challenge Level:2

The perimeter of a large triangle is 24 cm. What is the total length of the black lines used to draw the figure?

Weekly Problem 44 - 2009

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

A garden has the shape of a right-angled triangle. A fence goes from the corner with the right-angle to a point on the opposite side. How long is the fence?

Weekly Problem 29 - 2010

Stage: 3 Short Challenge Level: Challenge Level:1

An isosceles triangle is drawn inside another triangle. Can you work out the length of its base?

Weekly Problem 1 - 2011

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

Use facts about the angle bisectors of this triangle to work out another internal angle.

Weekly Problem 16 - 2011

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

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

Weekly Problem 27 - 2014

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

Weekly Problem 27 - 2014

Weekly Problem 32 - 2014

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

Weekly Problem 32 - 2014

Weekly Problem 37 - 2014

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

Weekly Problem 37 - 2014

Weekly Problem 41 - 2014

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

Weekly Problem 41 - 2014

Weekly Problem 8 - 2016

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

The diagram shows a quadrilateral ABCD, in which AD=BC, ∠CAD=50∘, ∠ACD=65∘ and ∠ACB=70∘. What is the size of ∠ABC?

Weekly Problem 17 - 2016

Stage: 4 Short Challenge Level: Challenge Level:1

The diagram shows an equilateral triangle touching two straight lines. What is the sum of the four marked angles?