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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?

Disappearing Square

Age 11 to 14
Challenge Level

The area of a triangle is found by multiplying the base by the height then halving your answer.

(Be careful not to use the length of a side but the height from base to apex.)

Could this be to do with the way the squares are drawn? Look out for the parts of squares and how they are matched up.