There are 70 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?
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 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?
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?
Wallpaper
Age 5 to 7
Challenge Level
These pieces of wallpaper need to be ordered from smallest to largest. Can you find a way to do it?
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?
Sizing Them Up
Age 5 to 7
Challenge Level
Can you put these shapes in order of size? Start with the smallest.
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.
Warmsnug Double Glazing
Age 14 to 16
Challenge Level
How have "Warmsnug" arrived at the prices shown on their windows? Which window has been given an incorrect price?
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?
Pythagoras for a Tetrahedron
Age 16 to 18
Challenge Level
In a right-angled tetrahedron prove that the sum of the squares of the areas of the 3 faces in mutually perpendicular planes equals the square of the area of the sloping face. A generalisation of. . . .
Semi-detached
Age 14 to 16
Challenge Level
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.
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?
Compare Areas
Age 14 to 16
Challenge Level
Which has the greatest area, a circle or a square, inscribed in an isosceles right angle triangle?
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.
The Square Under the Hypotenuse
Age 14 to 16
Challenge Level
Can you work out the side length of a square that just touches the hypotenuse of a right angled triangle?
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.
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?
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.
NRICH is part of the family of activities in the Millennium Mathematics Project.