Search by Topic

Resources tagged with Area similar to A Cartesian Puzzle:

Filter by: Content type:
Stage:
Challenge level:

There are 88 results

Broad Topics > Measures and Mensuration > Area

Shape Draw

Stage: 2 Challenge Level:

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

Triangle Island

Stage: 2 Challenge Level:

You have pitched your tent (the red triangle) on an island. Can you move it to the position shown by the purple triangle making sure you obey the rules?

Kissing Triangles

Stage: 3 Challenge Level:

Determine the total shaded area of the 'kissing triangles'.

Overlap

Stage: 3 Challenge Level:

A red square and a blue square overlap so that the corner of the red square rests on the centre of the blue square. Show that, whatever the orientation of the red square, it covers a quarter of the. . . .

Cutting it Out

Stage: 1 and 2 Challenge Level:

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

A Square in a Circle

Stage: 2 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?

Two Squared

Stage: 2 Challenge Level:

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?

Fit These Shapes

Stage: 1 and 2 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?

Shear Magic

Stage: 3 Challenge Level:

What are the areas of these triangles? What do you notice? Can you generalise to other "families" of triangles?

Fencing

Stage: 2 Challenge Level:

Arrange your fences to make the largest rectangular space you can. Try with four fences, then five, then six etc.

Numerically Equal

Stage: 2 Challenge Level:

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

How Random!

Stage: 2 Challenge Level:

Explore this interactivity and see if you can work out what it does. Could you use it to estimate the area of a shape?

Ribbon Squares

Stage: 2 Challenge Level:

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

Inside Seven Squares

Stage: 2 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?

Triangle Relations

Stage: 2 Challenge Level:

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

Wrapping Presents

Stage: 2 Challenge Level:

Choose a box and work out the smallest rectangle of paper needed to wrap it so that it is completely covered.

Cover the Tray

Stage: 2 Challenge Level:

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

Kite

Stage: 3 Challenge Level:

Derive a formula for finding the area of any kite.

Overlapping Squares

Stage: 2 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.

Tilted Squares

Stage: 3 Challenge Level:

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

Uncanny Triangles

Stage: 2 Challenge Level:

Can you help the children find the two triangles which have the lengths of two sides numerically equal to their areas?

Cylinder Cutting

Stage: 2 and 3 Challenge Level:

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

Lying and Cheating

Stage: 3 Challenge Level:

Follow the instructions and you can take a rectangle, cut it into 4 pieces, discard two small triangles, put together the remaining two pieces and end up with a rectangle the same size. Try it!

Rati-o

Stage: 3 Challenge Level:

Points P, Q, R and S each divide the sides AB, BC, CD and DA respectively in the ratio of 2 : 1. Join the points. What is the area of the parallelogram PQRS in relation to the original rectangle?

Pick's Theorem

Stage: 3 Challenge Level:

Polygons drawn on square dotty paper have dots on their perimeter (p) and often internal (i) ones as well. Find a relationship between p, i and the area of the polygons.

Fence It

Stage: 3 Challenge Level:

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

An Unusual Shape

Stage: 3 Challenge Level:

Can you maximise the area available to a grazing goat?

Approaches to Area

Stage: 1 and 2

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

Tiling

Stage: 2 Challenge Level:

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

Extending Great Squares

Stage: 2 and 3 Challenge Level:

Explore one of these five pictures.

Shaping It

Stage: 1 and 2 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.

Tiles in the Garden

Stage: 2 Challenge Level:

How many tiles do we need to tile these patios?

Tiling Into Slanted Rectangles

Stage: 2 and 3 Challenge Level:

A follow-up activity to Tiles in the Garden.

Through the Window

Stage: 2 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

Stage: 2 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?

Changing Areas, Changing Perimeters

Stage: 3 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?

Area and Perimeter

Stage: 2 Challenge Level:

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

A Day with Grandpa

Stage: 2 Challenge Level:

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

More Transformations on a Pegboard

Stage: 2 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.

Circle Panes

Stage: 2 Challenge Level:

Look at the mathematics that is all around us - this circular window is a wonderful example.

Rope Mat

Stage: 2 Challenge Level:

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

Growing Rectangles

Stage: 3 Challenge Level:

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

Making Rectangles

Stage: 2 and 3 Challenge Level:

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

Isosceles Triangles

Stage: 3 Challenge Level:

Draw some isosceles triangles with an area of $9$cm$^2$ and a vertex at (20,20). If all the vertices must have whole number coordinates, how many is it possible to draw?

Exploration Versus Calculation

Stage: 1, 2 and 3

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

The Pillar of Chios

Stage: 3 Challenge Level:

Semicircles are drawn on the sides of a rectangle ABCD. A circle passing through points ABCD carves out four crescent-shaped regions. Prove that the sum of the areas of the four crescents is equal to. . . .

Torn Shapes

Stage: 2 Challenge Level:

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

Carpet Cuts

Stage: 3 Challenge Level:

You have a 12 by 9 foot carpet with an 8 by 1 foot hole exactly in the middle. Cut the carpet into two pieces to make a 10 by 10 foot square carpet.

Pie Cuts

Stage: 3 Challenge Level:

Investigate the different ways of cutting a perfectly circular pie into equal pieces using exactly 3 cuts. The cuts have to be along chords of the circle (which might be diameters).

F'arc'tion

Stage: 3 Challenge Level:

At the corner of the cube circular arcs are drawn and the area enclosed shaded. What fraction of the surface area of the cube is shaded? Try working out the answer without recourse to pencil and. . . .