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#### Resources tagged with Area similar to Garden Fence:

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Broad Topics > Measures and Mensuration > Area

### 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?

### Bull's Eye

##### Stage: 3 Challenge Level:

What fractions of the largest circle are the two shaded regions?

### 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.

### It Must Be 2000

##### Stage: 2 Challenge Level:

Here are many ideas for you to investigate - all linked with the number 2000.

### 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?

### Being Determined - Primary Measures

##### Stage: 1 and 2 Challenge Level:

Measure problems at primary level that may require determination.

### Being Thoughtful - Primary Measures

##### Stage: 1 and 2 Challenge Level:

Measure problems at primary level that require careful consideration.

### Approaches to Area

##### Stage: 1 and 2

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

### 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.

### Lawn Border

##### Stage: 1 and 2 Challenge Level:

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?

### Transformations on a Pegboard

##### Stage: 2 Challenge Level:

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

### From One Shape to Another

##### Stage: 2

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.

### Being Collaborative - Primary Measures

##### Stage: 1 and 2 Challenge Level:

Measure problems for primary learners to work on with others.

### Numerically Equal

##### Stage: 2 Challenge Level:

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

### Circle Panes

##### Stage: 2 Challenge Level:

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

### 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?

### Shape Draw

##### Stage: 2 Challenge Level:

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

### 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?

### 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?

### Always, Sometimes or Never? Shape

##### Stage: 2 Challenge Level:

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

### Different Sizes

##### Stage: 1 and 2 Challenge Level:

A simple visual exploration into halving and doubling.

### Perimeter Possibilities

##### Stage: 3 Challenge Level:

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

### 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?

### The Pi Are Square

##### Stage: 3 Challenge Level:

A circle with the radius of 2.2 centimetres is drawn touching the sides of a square. What area of the square is NOT covered by the circle?

### Growing Rectangles

##### Stage: 3 Challenge Level:

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

### 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.

### Tiles in the Garden

##### Stage: 2 Challenge Level:

How many tiles do we need to tile these patios?

### Being Curious - Primary Measures

##### Stage: 1 and 2 Challenge Level:

Measure problems for inquiring primary learners.

### 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?

### 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?

### Can They Be Equal?

##### Stage: 3 Challenge Level:

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

### Square Pegs

##### Stage: 3 Challenge Level:

Which is a better fit, a square peg in a round hole or a round peg in a square hole?

### 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. . . .

### 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).

### Squaring the Circle

##### Stage: 3 Challenge Level:

Bluey-green, white and transparent squares with a few odd bits of shapes around the perimeter. But, how many squares are there of each type in the complete circle? Study the picture and make. . . .

### Warmsnug Double Glazing

##### Stage: 3 Challenge Level:

How have "Warmsnug" arrived at the prices shown on their windows? Which window has been given an incorrect price?

### The Big Cheese

##### Stage: 2 Challenge Level:

Investigate the area of 'slices' cut off this cube of cheese. What would happen if you had different-sized block of cheese to start with?

### Fencing Lambs

##### Stage: 2 Challenge Level:

A thoughtful shepherd used bales of straw to protect the area around his lambs. Explore how you can arrange the bales.

### Dissect

##### Stage: 3 Challenge Level:

It is possible to dissect any square into smaller squares. What is the minimum number of squares a 13 by 13 square can be dissected into?

### 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?

### Triangle Relations

##### Stage: 2 Challenge Level:

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

### Tiling

##### Stage: 2 Challenge Level:

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

### Cover the Tray

##### Stage: 2 Challenge Level:

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

### 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.

### Making Squares

##### Stage: 2

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?

### 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?

### Square Areas

##### Stage: 3 Challenge Level:

Can you work out the area of the inner square and give an explanation of how you did it?

### 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.

### Making Rectangles

##### Stage: 2 and 3 Challenge Level:

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