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Kissing Triangles

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

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?

More Isometric Areas

Age 11 to 14
Challenge Level


You might find it useful to take a look at Isometric Areas.

Can you see how you could join another identical (congruent) triangle to each triangle to form parallelograms?

How does the area of each triangle relate to the area of the parallelogram?