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Kissing Triangles

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

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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?

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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?

Triangular Tantaliser

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

You need to be systematic. Start with certain limitations (constraints) and exhaust all possibilities - try to justfy how you know there are no other triangles in this "category". Then extend your investigation to more categories.