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Kissing Triangles

Determine the total shaded area of the 'kissing triangles'.


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.


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?

Isosceles Triangles

Age 11 to 14 Challenge Level:

Isosceles triangles have two equal sides.

The area of a triangle is half the base times the height.

Any of the three vertices of the triangle can be at $(20, 20)$.

There are sets of identical (congruent) triangles with an area of $9$cm$^2$.
How many triangles are there in each set? How many sets?