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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

Draw all the possible distinct triangles on a 4 x 4 dotty grid.

Picture of a Geoboard with four rows of four pegs

N.B. Distinct triangles cannot be placed one over the other by translating, rotating or reflecting them.

Convince me that you have all possible triangles.