There are 71 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
Nine squares are fitted together to form a rectangle. Can you find its dimensions?
Are these statements always true, sometimes true or never true?
Can you work out the side length of a square that just touches the hypotenuse of a right angled triangle?
We started drawing some quadrilaterals - can you complete them?
Can you deduce the perimeters of the shapes from the information given?
Use the information on these cards to draw the shape that is being described.
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?
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?
What is the largest 'ribbon square' you can make? And the smallest? How many different squares can you make altogether?
I'm thinking of a rectangle with an area of 24. What could its perimeter be?
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?
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?
Can you rank these sets of quantities in order, from smallest to largest? Can you provide convincing evidence for your rankings?
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.
What can you say about these shapes? This problem challenges you to create shapes with different areas and perimeters.
A task which depends on members of the group noticing the needs of others and responding.
What happens to the area and volume of 2D and 3D shapes when you enlarge them?
Can you find rectangles where the value of the area is the same as the value of the perimeter?
These pieces of wallpaper need to be ordered from smallest to largest. Can you find a way to do it?
These rectangles have been torn. How many squares did each one have inside it before it was ripped?
Can you put these shapes in order of size? Start with the smallest.
Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.
How have "Warmsnug" arrived at the prices shown on their windows? Which window has been given an incorrect price?
If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?
It's easy to work out the areas of most squares that we meet, but what if they were tilted?
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 Pythagoras' Theorem.
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.
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?
How would you move the bands on the pegboard to alter these shapes?
Can you draw a square in which the perimeter is numerically equal to the area?
Which has the greatest area, a circle or a square, inscribed in an isosceles right angle triangle?
Cut differently-sized square corners from a square piece of paper to make boxes without lids. Do they all have the same volume?
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?
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.
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?
What is the total area of the four outside triangles which are outlined in red in this arrangement of squares inside each other?
How many centimetres of rope will I need to make another mat just like the one I have here?
Cut off three right angled isosceles triangles to produce a pentagon. With two lines, cut the pentagon into three parts which can be rearranged into another square.
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 the pictures.
Choose a box and work out the smallest rectangle of paper needed to wrap it so that it is completely covered.
If I use 12 green tiles to represent my lawn, how many different ways could I arrange them? How many border tiles would I need each time?
What happens to the area of a square if you double the length of the sides? Try the same thing with rectangles, diamonds and other shapes. How do the four smaller ones fit into the larger one?
Investigate how this pattern of squares continues. You could measure lengths, areas and angles.
Arrange your fences to make the largest rectangular space you can. Try with four fences, then five, then six etc.
A thoughtful shepherd used bales of straw to protect the area around his lambs. Explore how you can arrange the bales.
Investigate all the different squares you can make on this 5 by 5 grid by making your starting side go from the bottom left hand point. Can you find out the areas of all these squares?
What is the smallest number of tiles needed to tile this patio? Can you investigate patios of different sizes?
How many ways can you find of tiling the square patio, using square tiles of different sizes?
This practical challenge invites you to investigate the different squares you can make on a square geoboard or pegboard.