Resources tagged with: Area - squares and rectangles

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There are 60 NRICH Mathematical resources connected to Area - squares and rectangles, you may find related items under Measuring and calculating with units.

Broad Topics > Measuring and calculating with units > Area - squares and rectangles

Alison's Quilt

Age 11 to 14
Challenge Level

Nine squares are fitted together to form a rectangle. Can you find its dimensions?

Always, Sometimes or Never? Shape

Age 7 to 11
Challenge Level

Are these statements always true, sometimes true or never true?

Perimeter Challenge

Age 11 to 14
Challenge Level

Can you deduce the perimeters of the shapes from the information given?

Shape Draw

Age 7 to 11
Challenge Level

Use the information on these cards to draw the shape that is being described.

Through the Window

Age 7 to 11
Challenge Level

My local DIY shop calculates the price of its windows according to the area of glass and the length of frame used. Can you work out how they arrived at these prices?

Dicey Perimeter, Dicey Area

Age 7 to 11
Challenge Level

In this game for two players, you throw two dice and find the product. How many shapes can you draw on the grid which have that area or perimeter?

Ribbon Squares

Age 7 to 11
Challenge Level

What is the largest 'ribbon square' you can make? And the smallest? How many different squares can you make altogether?

Perimeter Possibilities

Age 11 to 14
Challenge Level

I'm thinking of a rectangle with an area of 24. What could its perimeter be?

Different Sizes

Age 5 to 11
Challenge Level

A simple visual exploration into halving and doubling.

Changing Areas, Changing Perimeters

Age 11 to 14
Challenge Level

How can you change the area of a shape but keep its perimeter the same? How can you change the perimeter but keep the area the same?

Poly Plug Rectangles

Age 5 to 14
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?

Shaping It

Age 5 to 11
Challenge Level

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.

Area and Perimeter

Age 7 to 11
Challenge Level

What can you say about these shapes? This problem challenges you to create shapes with different areas and perimeters.

Growing Rectangles

Age 11 to 14
Challenge Level

What happens to the area and volume of 2D and 3D shapes when you enlarge them?

Can They Be Equal?

Age 11 to 14
Challenge Level

Can you find rectangles where the value of the area is the same as the value of the perimeter?

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?

More Transformations on a Pegboard

Age 7 to 11
Challenge Level

Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.

Fence It

Age 11 to 14
Challenge Level

If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?

Tilted Squares

Age 11 to 14
Challenge Level

It's easy to work out the areas of most squares that we meet, but what if they were tilted?

Fitted

Age 7 to 11
Challenge Level

Nine squares with side lengths 1, 4, 7, 8, 9, 10, 14, 15, and 18 cm can be fitted together to form a rectangle. What are the dimensions of the rectangle?

Transformations on a Pegboard

Age 7 to 11
Challenge Level

How would you move the bands on the pegboard to alter these shapes?

Numerically Equal

Age 7 to 11
Challenge Level

Can you draw a square in which the perimeter is numerically equal to the area?

Making Boxes

Age 7 to 11
Challenge Level

Cut differently-sized square corners from a square piece of paper to make boxes without lids. Do they all have the same volume?

Pebbles

Age 7 to 11
Challenge Level

Place four pebbles on the sand in the form of a square. Keep adding as few pebbles as necessary to double the area. How many extra pebbles are added each time?

Paper Halving

Age 5 to 11
Challenge Level

In how many ways can you halve a piece of A4 paper? How do you know they are halves?

Being Resilient - Primary Measures

Age 5 to 11
Challenge Level

Measure problems at primary level that may require resilience.

Being Resourceful - Primary Measures

Age 5 to 11
Challenge Level

Measure problems at primary level that require careful consideration.

Being Collaborative - Primary Measures

Age 5 to 11
Challenge Level

Measure problems for primary learners to work on with others.

Being Curious - Primary Measures

Age 5 to 11
Challenge Level

Measure problems for inquiring primary learners.

Completing Quadrilaterals

Age 11 to 14
Challenge Level

We started drawing some quadrilaterals - can you complete them?

Cover the Tray

Age 7 to 11
Challenge Level

These practical challenges are all about making a 'tray' and covering it with paper.

Tiling Into Slanted Rectangles

Age 7 to 11
Challenge Level

A follow-up activity to Tiles in the Garden.

Tiles in the Garden

Age 7 to 11
Challenge Level

How many tiles do we need to tile these patios?

Cylinder Cutting

Age 7 to 11
Challenge Level

An activity for high-attaining learners which involves making a new cylinder from a cardboard tube.

Place Your Orders

Age 11 to 14
Challenge Level

Can you rank these sets of quantities in order, from smallest to largest? Can you provide convincing evidence for your rankings?

Extending Great Squares

Age 7 to 11
Challenge Level

Explore one of these five pictures.

Fit These Shapes

Age 5 to 11
Challenge Level

What is the largest number of circles we can fit into the frame without them overlapping? How do you know? What will happen if you try the other shapes?

Making Rectangles

Age 7 to 14
Challenge Level

A task which depends on members of the group noticing the needs of others and responding.

Cutting it Out

Age 5 to 11
Challenge Level

I cut this square into two different shapes. What can you say about the relationship between them?

Tiling

Age 7 to 11
Challenge Level

An investigation that gives you the opportunity to make and justify predictions.

A Day with Grandpa

Age 7 to 11
Challenge Level

Grandpa was measuring a rug using yards, feet and inches. Can you help William to work out its area?

Triangle Relations

Age 7 to 11
Challenge Level

What do these two triangles have in common? How are they related?

Overlapping Squares

Age 7 to 11
Challenge Level

Have a good look at these images. Can you describe what is happening? There are plenty more images like this on NRICH's Exploring Squares CD.

Approaches to Area

Age 5 to 11

This article for teachers gives some food for thought when teaching ideas about area.

Exploration Versus Calculation

Age 5 to 11

This article, written for teachers, discusses the merits of different kinds of resources: those which involve exploration and those which centre on calculation.

From One Shape to Another

Age 7 to 14

Read about David Hilbert who proved that any polygon could be cut up into a certain number of pieces that could be put back together to form any other polygon of equal area.

A Square in a Circle

Age 7 to 11
Challenge Level

What shape has Harry drawn on this clock face? Can you find its area? What is the largest number of square tiles that could cover this area?

Inside Seven Squares

Age 7 to 11
Challenge Level

What is the total area of the four outside triangles which are outlined in red in this arrangement of squares inside each other?

Rope Mat

Age 7 to 11
Challenge Level

How many centimetres of rope will I need to make another mat just like the one I have here?

Framed

Age 11 to 14
Challenge Level

Seven small rectangular pictures have one inch wide frames. The frames are removed and the pictures are fitted together like a jigsaw to make a rectangle of length 12 inches. Find the dimensions of. . . .