Triangles

problem
Farhan's poor square

Age

14 to 16

Challenge level

From the measurements and the clue given find the area of the square that is not covered by the triangle and the circle.
problem
Counting triangles

Age

11 to 14

Challenge level

Triangles are formed by joining the vertices of a skeletal cube. How many different types of triangle are there? How many triangles altogether?
problem
LOGO challenge 5 - patch

Age

11 to 16

Challenge level

Using LOGO, can you construct elegant procedures that will draw this family of 'floor coverings'?
problem
Threesomes

Age

11 to 14

Challenge level

Imagine an infinitely large sheet of square dotty paper on which you can draw triangles of any size you wish (providing each vertex is on a dot). What areas is it/is it not possible to draw?
problem
A shade crossed

Age

14 to 16

Challenge level

Find the area of the shaded region created by the two overlapping triangles in terms of a and b?
problem
ArRh!

Age

14 to 16

Challenge level

Triangle ABC is equilateral. D, the midpoint of BC, is the centre of the semi-circle whose radius is R which touches AB and AC, as well as a smaller circle with radius r which also touches AB and AC. What is the value of r/R?
problem
Dotty triangles

Age

11 to 14

Challenge level

Imagine an infinitely large sheet of square dotty paper on which you can draw triangles of any size you wish (providing each vertex is on a dot). What areas is it/is it not possible to draw?
problem
Isosceles meld

Age

11 to 14

Challenge level

Weekly Problem 9 - 2012
What is the angle QPT in this diagram?
problem
Centred

Age

14 to 16

Challenge level

Weekly Problem 13 - 2012
The diagram shows contains some equal lengths. Can you work out one of the angles?
problem
Stellar angles

Age

11 to 14

Challenge level

Weekly Problem 30 - 2013
What is the angle $x$ in the star shape shown?