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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.
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?
Age 11 to 14 Short Challenge Level:
The diagonal of a unit square is used as one of the sides of a new square.
What is the area of this new square?
(A unit square is a square whose sides all have length 1 unit, and so its area is 1 square unit)
This problem is taken from the World Mathematics Championships
What is the area of this new square?
(A unit square is a square whose sides all have length 1 unit, and so its area is 1 square unit)
This problem is taken from the World Mathematics Championships
You can find more short problems, arranged by curriculum topic, in our short problems collection.
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NRICH is part of the family of activities in the Millennium Mathematics Project.
NRICH is part of the family of activities in the Millennium Mathematics Project.