Triangles

problem
Tetrahedra tester

Age

14 to 16

Challenge level

An irregular tetrahedron is composed of four different triangles. Can such a tetrahedron be constructed where the side lengths are 4, 5, 6, 7, 8 and 9 units of length?
problem
Triangle in a triangle

Age

14 to 16

Challenge level

Can you work out the fraction of the original triangle that is covered by the inner triangle?
problem
The square hole

Age

14 to 16

Challenge level

If the yellow equilateral triangle is taken as the unit for area, what size is the hole ?
problem
Lens angle

Age

14 to 16

Challenge level

Find the missing angle between the two secants to the circle when the two angles at the centre subtended by the arcs created by the intersections of the secants and the circle are 50 and 120 degrees.
problem
Hexy-metry

Age

14 to 16

Challenge level

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

Age

14 to 18

Challenge level

Find the sides of an equilateral triangle ABC where a trapezium BCPQ is drawn with BP=CQ=2 , PQ=1 and AP+AQ=sqrt7 . Note: there are 2 possible interpretations.
problem
Calculating with cosines

Age

14 to 18

Challenge level

If I tell you two sides of a right-angled triangle, you can easily work out the third. But what if the angle between the two sides is not a right angle?
problem
Impossible triangles?

Age

16 to 18

Challenge level

Which of these triangular jigsaws are impossible to finish?