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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.

Linkage

Four rods, two of length a and two of length b, are linked to form a kite. The linkage is moveable so that the angles change. What is the maximum area of the kite?

Estimating Angles

How good are you at estimating angles?

Add All the Angles

Age 11 to 14 Short Challenge Level:

Each letter in this diagram represents the angle between the two lines framing it.

What is the sum of all of the angles denoted by letters?





This problem is adapted from the World Mathematics Championships
You can find more short problems, arranged by curriculum topic, in our short problems collection.