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#### Resources tagged with Area similar to Gutter:

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### There are 84 results

Broad Topics > Measures and Mensuration > Area

### Gutter

##### Stage: 4 Challenge Level:

Manufacturers need to minimise the amount of material used to make their product. What is the best cross-section for a gutter?

### Of All the Areas

##### Stage: 4 Challenge Level:

Can you find a general rule for finding the areas of equilateral triangles drawn on an isometric grid?

### Max Box

##### Stage: 4 Challenge Level:

Three rods of different lengths form three sides of an enclosure with right angles between them. What arrangement maximises the area

### 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?

### Diagonals for Area

##### Stage: 4 Challenge Level:

Can you prove this formula for finding the area of a quadrilateral from its diagonals?

### 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. . . .

### Bound to Be

##### Stage: 4 Challenge Level:

Four quadrants are drawn centred at the vertices of a square . Find the area of the central region bounded by the four arcs.

### 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.

### Uniform Units

##### Stage: 4 Challenge Level:

Can you choose your units so that a cube has the same numerical value for it volume, surface area and total edge length?

##### 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.

### Areas of Parallelograms

##### Stage: 4 Challenge Level:

Can you find the area of a parallelogram defined by two vectors?

### 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.

### Same Height

##### Stage: 4 Challenge Level:

A trapezium is divided into four triangles by its diagonals. Suppose the two triangles containing the parallel sides have areas a and b, what is the area of the trapezium?

### Percentage Unchanged

##### Stage: 4 Challenge Level:

If the base of a rectangle is increased by 10% and the area is unchanged, by what percentage (exactly) is the width decreased by ?

### Dividing the Field

##### Stage: 4 Challenge Level:

A farmer has a field which is the shape of a trapezium as illustrated below. To increase his profits he wishes to grow two different crops. To do this he would like to divide the field into two. . . .

### Two Shapes & Printer Ink

##### Stage: 4 Challenge Level:

If I print this page which shape will require the more yellow ink?

### Square Pizza

##### Stage: 4 Challenge Level:

Can you show that you can share a square pizza equally between two people by cutting it four times using vertical, horizontal and diagonal cuts through any point inside the square?

### 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?

### 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?

### Squ-areas

##### Stage: 4 Challenge Level:

Three squares are drawn on the sides of a triangle ABC. Their areas are respectively 18 000, 20 000 and 26 000 square centimetres. If the outer vertices of the squares are joined, three more. . . .

### Areas and Ratios

##### Stage: 4 Challenge Level:

What is the area of the quadrilateral APOQ? Working on the building blocks will give you some insights that may help you to work it out.

### 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.

### 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?

### 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?

### 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?

### 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.

### Perimeter Possibilities

##### Stage: 3 Challenge Level:

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

### Doesn't Add Up

##### Stage: 4 Challenge Level:

In this problem we are faced with an apparently easy area problem, but it has gone horribly wrong! What happened?

### 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?

##### 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. . . .

### 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?

### 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?

### 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.

### 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?

### Trapezium Four

##### Stage: 4 Challenge Level:

The diagonals of a trapezium divide it into four parts. Can you create a trapezium where three of those parts are equal in area?

### 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?

### 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?

### Towering Trapeziums

##### Stage: 4 Challenge Level:

Can you find the areas of the trapezia in this sequence?

### Making Rectangles

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

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

### Partly Circles

##### Stage: 4 Challenge Level:

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

### An Unusual Shape

##### Stage: 3 Challenge Level:

Can you maximise the area available to a grazing goat?

### 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?

### 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?

### Rhombus in Rectangle

##### Stage: 4 Challenge Level:

Take any rectangle ABCD such that AB > BC. The point P is on AB and Q is on CD. Show that there is exactly one position of P and Q such that APCQ is a rhombus.

### 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.

### 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?

### 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 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?

### Compare Areas

##### Stage: 4 Challenge Level:

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