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#### Resources tagged with Area similar to Squaring the Circle:

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Broad Topics > Measures and Mensuration > Area

### 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. . . .

### 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?

### 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).

### Bull's Eye

##### Stage: 3 Challenge Level:

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

### 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?

### 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!

### 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?

### Cylinder Cutting

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

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

### 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.

### Covering Cups

##### Stage: 3 Challenge Level:

What is the shape and dimensions of a box that will contain six cups and have as small a surface area as possible.

### 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?

### 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. . . .

### Tiling Into Slanted Rectangles

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

A follow-up activity to Tiles in the Garden.

### Extending Great Squares

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

Explore one of these five pictures.

### 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.

### Kite

##### Stage: 3 Challenge Level:

Derive a formula for finding the area of any kite.

### Making Rectangles

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

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

### Kissing Triangles

##### Stage: 3 Challenge Level:

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

### Growing Rectangles

##### Stage: 3 Challenge Level:

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

### 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?

### Towers

##### Stage: 3 Challenge Level:

A tower of squares is built inside a right angled isosceles triangle. The largest square stands on the hypotenuse. What fraction of the area of the triangle is covered by the series of squares?

### Great Squares

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

Investigate how this pattern of squares continues. You could measure lengths, areas and angles.

### Isosceles

##### Stage: 3 Challenge Level:

Prove that a triangle with sides of length 5, 5 and 6 has the same area as a triangle with sides of length 5, 5 and 8. Find other pairs of non-congruent isosceles triangles which have equal areas.

### 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?

### Crescents and Triangles

##### Stage: 4 Challenge Level:

Triangle ABC is right angled at A and semi circles are drawn on all three sides producing two 'crescents'. Show that the sum of the areas of the two crescents equals the area of triangle ABC.

### Poly-puzzle

##### Stage: 3 Challenge Level:

This rectangle is cut into five pieces which fit exactly into a triangular outline and also into a square outline where the triangle, the rectangle and the square have equal areas.

### Semi-detached

##### Stage: 4 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.

### Hallway Borders

##### Stage: 3 Challenge Level:

A hallway floor is tiled and each tile is one foot square. Given that the number of tiles around the perimeter is EXACTLY half the total number of tiles, find the possible dimensions of the hallway.

### Blue and White

##### Stage: 3 Challenge Level:

Identical squares of side one unit contain some circles shaded blue. In which of the four examples is the shaded area greatest?

### Appearing Square

##### Stage: 3 Challenge Level:

Make an eight by eight square, the layout is the same as a chessboard. You can print out and use the square below. What is the area of the square? Divide the square in the way shown by the red dashed. . . .

### Curvy Areas

##### Stage: 4 Challenge Level:

Have a go at creating these images based on circles. What do you notice about the areas of the different sections?

### 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?

### 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.

### Partly Circles

##### Stage: 4 Challenge Level:

What is the same and what is different about these circle questions? What connections can you make?

##### Stage: 4 Challenge Level:

Given a square ABCD of sides 10 cm, and using the corners as centres, construct four quadrants with radius 10 cm each inside the square. The four arcs intersect at P, Q, R and S. Find the. . . .

### Compare Areas

##### Stage: 4 Challenge Level:

Which has the greatest area, a circle or a square inscribed in an isosceles, right angle triangle?

### Two Circles

##### Stage: 4 Challenge Level:

Draw two circles, each of radius 1 unit, so that each circle goes through the centre of the other one. What is the area of the overlap?

### Inscribed in a Circle

##### Stage: 4 Challenge Level:

The area of a square inscribed in a circle with a unit radius is, satisfyingly, 2. What is the area of a regular hexagon inscribed in a circle with a unit radius?

### An Unusual Shape

##### Stage: 3 Challenge Level:

Can you maximise the area available to a grazing goat?

### Perimeter Possibilities

##### Stage: 3 Challenge Level:

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

### Six Discs

##### Stage: 4 Challenge Level:

Six circular discs are packed in different-shaped boxes so that the discs touch their neighbours and the sides of the box. Can you put the boxes in order according to the areas of their bases?

### Maths Filler

##### Stage: 3 Challenge Level:

Imagine different shaped vessels being filled. Can you work out what the graphs of the water level should look like?

### Equilateral Areas

##### Stage: 4 Challenge Level:

ABC and DEF are equilateral triangles of side 3 and 4 respectively. Construct an equilateral triangle whose area is the sum of the area of ABC and DEF.

##### Stage: 4 Challenge Level:

Investigate the properties of quadrilaterals which can be drawn with a circle just touching each side and another circle just touching each vertex.

### 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?

### Efficient Packing

##### Stage: 4 Challenge Level:

How efficiently can you pack together disks?

### 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?

### Salinon

##### Stage: 4 Challenge Level:

This shape comprises four semi-circles. What is the relationship between the area of the shaded region and the area of the circle on AB as diameter?

### Semi-square

##### Stage: 4 Challenge Level:

What is the ratio of the area of a square inscribed in a semicircle to the area of the square inscribed in the entire circle?