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Which is a better fit, a square peg in a round hole or a round peg in a square hole?

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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.

Rectangle Dissection

Age 11 to 14 Short Challenge Level:

The 16 by 9 rectangle is cut as shown.

16 by 9 rectangle cut into pieces

If the pieces are rearranged to form a square, what is the perimeter of the square?

 

If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.
 

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