Being resourceful

Which has the greatest area, a circle or a square, inscribed in an isosceles right angle triangle?

Is it possible to have a tetrahedron whose six edges have lengths 10, 20, 30, 40, 50 and 60 units?

A napkin is folded so that a corner coincides with the midpoint of an opposite edge. Investigate the three triangles formed.

A hexagon, with sides alternately a and b units in length, is inscribed in a circle. How big is the radius of the circle?

Using a ruler, pencil and compasses only, it is possible to construct a square inside any triangle so that all four vertices touch the sides of the triangle.

An observer is on top of a lighthouse. How far from the foot of the lighthouse is the horizon that the observer can see?

Can you see how to build a harmonic triangle? Can you work out the next two rows?

Can you find an efficent way to mix paints in any ratio?

If a sum invested gains 10% each year how long before it has doubled its value?

A plastic funnel is used to pour liquids through narrow apertures. What shape funnel would use the least amount of plastic to manufacture for any specific volume ?