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Isosceles

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.

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Trice

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?

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Floored

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?

Kissing Triangles

Age 11 to 14 Challenge Level:

The solution is 18 square centimetres and everyone who submitted a response got it right. Of special mention was the work of Sarah at Hethersett High School and Bryony with Sarah from Maidstone Girls' Grammar, all of whom had painstakingly set out their solutions complete with annotations and diagrams.

Some people managed to spot that it there are multiple ways of drawing the shape; the point in the middle where the triangles 'kiss' can be moved left or right! Well done to those who realised that despite the variety of ways of drawing the shape, the area is always 18 cm2Brilliant!