2D shapes and their properties

There are 152 NRICH Mathematical resources connected to 2D shapes and their properties

problem

Favourite

What's happening?

Age

5 to 7

Challenge level

Shapes are added to other shapes. Can you see what is happening? What is the rule?

problem

Favourite

Olympic rings

Age

5 to 7

Challenge level

Can you design your own version of the Olympic rings, using interlocking squares instead of circles?

problem

Favourite

National flags

Age

7 to 11

Challenge level

This problem explores the shapes and symmetries in some national flags.

problem

Favourite

Poly plug rectangles

Age

5 to 11

Challenge level

The computer has made a rectangle and will tell you the number of spots it uses in total. Can you find out where the rectangle is?

problem

Favourite

Track design

Age

14 to 16

Challenge level

Where should runners start the 200m race so that they have all run the same distance by the finish?

problem

Favourite

Seeing squares

Age

5 to 11

Challenge level

Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form a square.

problem

Favourite

Orthogonal circle

Age

16 to 18

Challenge level

Given any three non intersecting circles in the plane find another circle or straight line which cuts all three circles orthogonally.

problem

Favourite

Rolling around

Age

11 to 14

Challenge level

A circle rolls around the outside edge of a square so that its circumference always touches the edge of the square. Can you describe the locus of the centre of the circle?

problem

Favourite

Salinon

Age

14 to 16

Challenge level

This shape comprises four semi-circles. What is the relationship between the area of the shaded region and the area of the circle on AB as diameter?

problem

Favourite

Trapezium four

Age

14 to 16

Challenge level

The diagonals of a trapezium divide it into four parts. Can you create a trapezium where three of those parts are equal in area?

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For younger learners

2D shapes and their properties

What's happening?

Olympic rings

National flags

Poly plug rectangles

Track design

Seeing squares

Orthogonal circle

Rolling around

Salinon

Trapezium four