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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?
Age 11 to 14
Challenge Level
How many triangles are there in a parallelogram with side lengths
1 and 1?
2 and 1?
3 and 1?...
If you double one of the lengths, what would happen to the area?
If you double both of the lengths, what would happen to the area?
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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.