Geometrical Reasoning Stage 4 - Short Problems


This is part of our collection of Short Problems.

You may also be interested in our longer problems on Geometrical Reasoning - Stage 4.

Printable worksheets containing selections of these problems are available here:

Stage 4 ★★ Sheet 1 Solutions
  Sheet 2 Solutions

Eulerian

KS 3 & 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?

Centred

KS 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

KS 4 Short Challenge Level:

Challenge Level:2 Challenge Level:2

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

Inscribed Semicircle

KS 4 Short Challenge Level:

Challenge Level:2 Challenge Level:2

Weekly Problem 43 - 2017
The diagram shows a semicircle inscribed in a right angled triangle. What is the radius of the semicircle?

Incentre Angle

KS 4 Short Challenge Level:

Challenge Level:2 Challenge Level:2

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

Two Right Angles

KS 4 Short Challenge Level:

Challenge Level:2 Challenge Level:2

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

3-4-5 Circle

KS 4 Short Challenge Level:

Challenge Level:2 Challenge Level:2

Can you find the radius of the circle inscribed inside a '3-4-5 triangle'?

Quarters

KS 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?

Angle to Chord

KS 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?

Slide Height

KS 4 Short Challenge Level:

Challenge Level:2 Challenge Level:2

How high is the top of the slide?

Internal - External

KS 4 Short Challenge Level:

Challenge Level:2 Challenge Level:2

Weekly Problem 12 - 2016
The diagram shows a square PQRS and two equilateral triangles RSU and PST. PQ has length 1. What is the length of TU?

Shaded Square

KS 4 Short Challenge Level:

Challenge Level:2 Challenge Level:2

Weekly Problem 41 - 2016
The diagram shows a square, with lines drawn from its centre. What is the shaded area?

Isosceles Reduction

KS 4 Short Challenge Level:

Challenge Level:2 Challenge Level:2

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

Griddy Region

KS 4 Short Challenge Level:

Challenge Level:3 Challenge Level:3 Challenge Level:3

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

Cut-up Square

KS 4 Short Challenge Level:

Challenge Level:3 Challenge Level:3 Challenge Level:3

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

Garden Fence

KS 4 Short Challenge Level:

Challenge Level:3 Challenge Level:3 Challenge Level:3

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

KS 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?