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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.

Trice

ABCDEFGH is a 3 by 3 by 3 cube. Point P is 1/3 along AB (that is AP : PB = 1 : 2), point Q is 1/3 along GH and point R is 1/3 along ED. What is the area of the triangle PQR?

Ratty

If you know the sizes of the angles marked with coloured dots in this diagram which angles can you find by calculation?

Kissing Triangles

Age 11 to 14 Challenge Level:
Determine the total area of the two kissing triangles shaded red.


Is there more than one way of drawing the shape?