Construction - Short Problems


This is part of our collection of Short Problems.

You may also be interested in our longer problems on Construction.

Printable worksheets containing selections of these problems are available here:

Stage 4 ★ Sheet 1 Solutions

Defined Distances

Age 11 to 14 Short Challenge Level:

Mark writes four points on a line at different lengths. What is the distance between the two points furthest apart?

Contact Circles

Age 11 to 14 Short Challenge Level:

Weekly Problem 25 - 2010
These four touching circles have another circle hiding amongst them...

Folded A4

Age 11 to 14 Short Challenge Level:

Weekly Problem 45 - 2011
What shapes can be made by folding an A4 sheet of paper only once?

Either Side

Age 11 to 14 Short Challenge Level:

Weekly Problem 7 - 2012
A disc with a pencil inside it is rolled around the outside and inside of a wire equilateral triangle. What shape is drawn by the pencil?

Pink and White

Age 11 to 14 Short Challenge Level:

Weekly Problem 36 - 2013
The white square slides once around the pink square. Through what distance does the point P on the white square move?

Snail's Pace

Age 14 to 16 Short Challenge Level:

A snail is at the corner of a cube. What proportion of the cube's surface can the snail reach within an hour?

Triangular Wheel

Age 14 to 16 Short Challenge Level:

Weekly Problem 36 - 2014
An equilateral triangle is rolled along a line. What is the length of the path traced out by one of its vertices?

3-sided

Age 14 to 16 Short Challenge Level:

How many triangles can Jack draw with two sides of lengths $6$cm and $8$cm and an area of $7$cm$^2$?