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?

Rati-o

Age 11 to 14 Challenge Level:

An additional challenge here is to show that the inscribed polygon
is a parallelogram. Invite students to make conjectures about the
shape of this quadrilateral and then to prove their
conjectures.