Dotty Triangles
Imagine an infinitely large
sheet of square dotty paper on which you can draw triangles of any
size you wish (providing each vertex is on a dot). What areas is
it/is it not possible to draw?
Can you draw triangles of area 1, 2, 3, ?.. square
units?
Can you draw a triangle with an area of 1.5 square units?
What is the area of the smallest triangle you can draw? Is this triangle unique?
How many triangles of of area 2 square units can you draw and can you create "families" or "groups" of these triangles?
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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.
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?