This is part of our Secondary Curriculum collection of favourite rich tasks arranged by topic.

Scroll down to see the complete collection, or explore our subcollections on Perimeter and Area in two dimensions, and Surface Area and Volume in three dimensions.

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Favourite

### Tilted Squares

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

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Favourite

### Garden Shed

Can you minimise the amount of wood needed to build the roof of my garden shed?

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Favourite

### Where is the dot?

A dot starts at the point (1,0) and turns anticlockwise. Can you estimate the height of the dot after it has turned through 45 degrees? Can you calculate its height?

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Favourite

### Semi-detached

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.

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Favourite

### Inscribed in a Circle

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?

problem

Favourite

### The Spider and the Fly

A spider is sitting in the middle of one of the smallest walls in a
room and a fly is resting beside the window. What is the shortest
distance the spider would have to crawl to catch the fly?

problem

Favourite

### Where to Land

Chris is enjoying a swim but needs to get back for lunch. How far along the bank should she land?

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Favourite

### Ladder and Cube

A 1 metre cube has one face on the ground and one face against a
wall. A 4 metre ladder leans against the wall and just touches the
cube. How high is the top of the ladder above the ground?

problem

Favourite

### Bendy Quad

Four rods are hinged at their ends to form a convex quadrilateral.
Investigate the different shapes that the quadrilateral can take.
Be patient this problem may be slow to load.

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Favourite

### Compare Areas

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

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Favourite

### Hexy-Metry

A hexagon, with sides alternately a and b units in length, is inscribed in a circle. How big is the radius of the circle?

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Favourite

### Far Horizon

An observer is on top of a lighthouse. How far from the foot of the lighthouse is the horizon that the observer can see?

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Favourite

### Three by One

There are many different methods to solve this geometrical problem - how many can you find?

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Favourite

### Cubestick

Stick some cubes together to make a cuboid. Find two of the angles
by as many different methods as you can devise.

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*ou may also be interested in this collection of activities from the STEM Learning website, that complement the NRICH activities above.*