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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.


ABCDEFGH is a 3 by 3 by 3 cube. Point P is 1/3 along AB (that is AP : PB = 1 : 2), point Q is 1/3 along GH and point R is 1/3 along ED. What is the area of the triangle PQR?


If you know the sizes of the angles marked with coloured dots in this diagram which angles can you find by calculation?

Kissing Triangles

Age 11 to 14
Challenge Level
Try drawing a diagram of the shape for yourself, making sure it's to scale. See if you can find the area of some parts of the shape first.

You may wish to use GeoGebra to investigate the shape further.