Angles in polygons

problem

Darts and Kites

Age

14 to 16

Challenge level

1 out of 3

Explore the geometry of these dart and kite shapes!
problem

Golden Triangle

Age

16 to 18

Challenge level

2 out of 3

Three triangles ABC, CBD and ABD (where D is a point on AC) are all isosceles. Find all the angles. Prove that the ratio of AB to BC is equal to the golden ratio.
problem

Floored

Age

14 to 16

Challenge level

2 out of 3

A floor is covered by a tessellation of equilateral triangles, each having three equal arcs inside it. What proportion of the area of the tessellation is shaded?
problem

Tricircle

Age

14 to 16

Challenge level

2 out of 3

The centre of the larger circle is at the midpoint of one side of an equilateral triangle and the circle touches the other two sides of the triangle. A smaller circle touches the larger circle and two sides of the triangle. If the small circle has radius 1 unit find the radius of the larger circle.
problem

At a Glance

Age

14 to 16

Challenge level

3 out of 3

The area of a regular pentagon looks about twice as a big as the pentangle star drawn within it. Is it?
problem

Three Triangles

Age

7 to 11

Challenge level

1 out of 3

What do you notice when you put three triangles together?
problem

Possible Pairs

Age

7 to 11

Challenge level

1 out of 3

In this game, you turn over two cards and try to draw a triangle which has both properties.
problem

Data Duos

Age

7 to 11

Challenge level

1 out of 3

Can you match the Venn diagram with the Carroll diagram that shows the same information?
problem

Timber!

Age

7 to 11

Challenge level

2 out of 3

How can the school caretaker be sure that the tree would miss the school buildings if it fell?
problem

Fred the Class Robot

Age

7 to 11

Challenge level

2 out of 3

Billy's class had a robot called Fred who could draw with chalk held underneath him. What shapes did the pupils make Fred draw?