Geometrical Reasoning Stage 4- Short Problems

A collection of short Stage 4 problems on geometrical reasoning



Long Shadows

Stage: 3 Short Challenge Level: Challenge Level:1

Weekly Problem 10 - 2012
If you know how long Meg's shadow is, can you work out how long the shadow is when she stands on her brother's shoulders?

Centred

Stage: 4 Short Challenge Level: Challenge Level:1

Weekly Problem 13 - 2012
The diagram shows contains some equal lengths. Can you work out one of the angles?

Diagonal Touch

Stage: 3 Short Challenge Level: Challenge Level:1

Weekly Problem 21 - 2012
Two rectangles are drawn in a rectangle. What fraction of the rectangle is shaded?

Dodecagon Angle

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

Weekly Problem 50 - 2012
The diagram shows a regular dodecagon. What is the size of the marked angle?

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?

Two Right Angles

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

Weekly Problem 4 - 2008
In the figure given in the problem, calculate the length of an edge.

Angle to Chord

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

Weekly Problem 23 - 2008
A triangle has been drawn inside this circle. Can you find the length of the chord it forms?

Griddy Region

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

Weekly Problem 34 - 2008
What is the area of the region common to this triangle and square?

Garden Fence

Stage: 4 Short Challenge Level: Challenge Level:1

Weekly Problem 44 - 2009
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?

Altitude Inequalities

Stage: 4 Short Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Weekly Problem 8 - 2010
Are you able to find triangles such that these five statements are true?

Isoscles Reduction

Stage: 3 Short Challenge Level: Challenge Level:1

Weekly Problem 29 - 2010
An isosceles triangle is drawn inside another triangle. Can you work out the length of its base?

Incentre Angle

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

Weekly Problem 1 - 2011
Use facts about the angle bisectors of this triangle to work out another internal angle.

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?

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?

Quarters

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

Weekly Problem 27 - 2014
Four congruent isosceles trapezia are placed in a square. What fraction of the square is shaded?

Intersecting Squares

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

Weekly Problem 32 - 2014
Three overlapping squares are shown. If you know the areas of the overlapping and non-overlapping parts, can you work out the side lengths of the squares?

Eulerian

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

Weekly Problem 37 - 2014
Which of the five diagrams below could be drawn without taking the pen off the page and without drawing along a line already drawn?

Radioactive Triangle

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

Weekly Problem 41 - 2014
Three straight lines divide an equilateral triangle into seven regions. What is the side length of the original triangle?

Cut-up Square

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

Weekly Problem 15 - 2015
In the diagram, two lines have been draawn in a square. What is the ratio of the areas marked?