There are **118** NRICH Mathematical resources connected to **2D shapes and their properties**, you may find related items under Angles, Polygons, and Geometrical Proof.

Are these statements relating to calculation and properties of shapes always true, sometimes true or never true?

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

This problem is intended to get children to look really hard at something they will see many times in the next few months.

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?

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

These pictures were made by starting with a square, finding the half-way point on each side and joining those points up. You could investigate your own starting shape.

This interactivity allows you to sort logic blocks by dragging their images.

This challenge invites you to create your own picture using just straight lines. Can you identify shapes with the same number of sides and decorate them in the same way?

This task develops spatial reasoning skills. By framing and asking questions a member of the team has to find out what mathematical object they have chosen.

Can you each work out what shape you have part of on your card? What will the rest of it look like?

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

What shape is the overlap when you slide one of these shapes half way across another? Can you picture it in your head? Use the interactivity to check your visualisation.

The red ring is inside the blue ring in this picture. Can you rearrange the rings in different ways? Perhaps you can overlap them or put one outside another?

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

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

Draw three equal line segments in a unit circle to divide the circle into four parts of equal area.

Choose the size of your pegboard and the shapes you can make. Can you work out the strategies needed to block your opponent?

Use a single sheet of A4 paper and make a cylinder having the greatest possible volume. The cylinder must be closed off by a circle at each end.

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?

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?

A square of area 40 square cms is inscribed in a semicircle. Find the area of the square that could be inscribed in a circle of the same radius.

Use the isometric grid paper to find the different polygons.

By inscribing a circle in a square and then a square in a circle find an approximation to pi. By using a hexagon, can you improve on the approximation?

Identical squares of side one unit contain some circles shaded blue. In which of the four examples is the shaded area greatest?

Explain how the thirteen pieces making up the regular hexagon shown in the diagram can be re-assembled to form three smaller regular hexagons congruent to each other.

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. . . .

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

Ten squares form regular rings either with adjacent or opposite vertices touching. Calculate the inner and outer radii of the rings that surround the squares.

A small circle fits between two touching circles so that all three circles touch each other and have a common tangent? What is the exact radius of the smallest circle?

Arrange the shapes in a line so that you change either colour or shape in the next piece along. Can you find several ways to start with a blue triangle and end with a red circle?

Can you sketch triangles that fit in the cells in this grid? Which ones are impossible? How do you know?

Here is a selection of different shapes. Can you work out which ones are triangles, and why?

What shape is made when you fold using this crease pattern? Can you make a ring design?

Can you find the areas of the trapezia in this sequence?

'What Shape?' activity for adult and child. Can you ask good questions so you can work out which shape your partner has chosen?

Can Jo make a gym bag for her trainers from the piece of fabric she has?

What shapes should Elly cut out to make a witch's hat? How can she make a taller hat?

Can you spot circles, spirals and other types of curves in these photos?

Look at some of the patterns in the Olympic Opening ceremonies and see what shapes you can spot.

Investigate constructible images which contain rational areas.

If these balls are put on a line with each ball touching the one in front and the one behind, which arrangement makes the shortest line of balls?

Can you recreate squares and rhombuses if you are only given a side or a diagonal?

Investigate the properties of quadrilaterals which can be drawn with a circle just touching each side and another circle just touching each vertex.

What do you think is the same about these two Logic Blocks? What others do you think go with them in the set?

This activity challenges you to make collections of shapes. Can you give your collection a name?

Are all the possible combinations of two shapes included in this set of 27 cards? How do you know?

This article describes investigations that offer opportunities for children to think differently, and pose their own questions, about shapes.

A cheap and simple toy with lots of mathematics. Can you interpret the images that are produced? Can you predict the pattern that will be produced using different wheels?

A spiropath is a sequence of connected line segments end to end taking different directions. The same spiropath is iterated. When does it cycle and when does it go on indefinitely?