2D shapes and their properties

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

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?

problem

Favourite

Where are they?

Age

7 to 11

Challenge level

Use the isometric grid paper to find the different polygons.

problem

Favourite

Square it

Age

11 to 16

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

Torn shapes

Age

7 to 11

Challenge level

These rectangles have been torn. How many squares did each one have inside it before it was ripped?

problem

Favourite

Four triangles puzzle

Age

5 to 11

Challenge level

Cut four triangles from a square as shown in the picture. How many different shapes can you make by fitting the four triangles back together?

problem

Favourite

Given a square ABCD of sides 10 cm, and using the corners as centres, construct four quadrants with radius 10 cm each inside the square. The four arcs intersect at P, Q, R and S. Find the area enclosed by PQRS.

problem

Favourite

Curvy areas

Age

14 to 16

Challenge level

Have a go at creating these images based on circles. What do you notice about the areas of the different sections?

problem

Favourite

Move those halves

Age

7 to 11

Challenge level

For this task, you'll need an A4 sheet and two A5 transparent sheets. Decide on a way of arranging the A5 sheets on top of the A4 sheet and explore ...

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For younger learners

2D shapes and their properties

Rolling around

Salinon

Trapezium four

Where are they?

Square it

Torn shapes

Four triangles puzzle

Quadarc

Curvy areas

Move those halves