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Kissing Triangles

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

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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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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?

Shapely Pairs

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3
You're going to have to come up with a system to make sure that you don't miss out any pairs, and to make sure that you don't count any twice. You could pick one card and see how many other cards could be paired with it, to get you started.

Is it possible to pair all the cards? Try playing around with different possibilities. You might have to pair up some cards first, if they don't have many possible partners.