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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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Linkage

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Tricky Tessellations

Age 11 to 14 Short Challenge Level:




The figure shows part of a tiling, which extends indefinitely in every direction across the whole plane.

Each tile is a regular hexagon.

Some of the tiles are white, the others are black.

What fraction of the plane is black?







This problem is taken from the UKMT Mathematical Challenges.
You can find more short problems, arranged by curriculum topic, in our short problems collection.