Follow the hints and prove Pick's Theorem.
Join in this ongoing research. Build squares on the sides of a triangle, join the outer vertices forming hexagons, build further rings of squares and quadrilaterals, investigate.
Change the squares in this diagram and spot the property that stays the same for the triangles. Explain...
Find a quadratic formula which generalises Pick's Theorem.
A square of area 40 square cms is inscribed in a semicircle. Find the area of the square that could be inscribed in a circle of the same radius.
Which has the greatest area, a circle or a square inscribed in an isosceles, right angle triangle?
Cut off three right angled isosceles triangles to produce a pentagon. With two lines, cut the pentagon into three parts which can be rearranged into another square.
In a right-angled tetrahedron prove that the sum of the squares of the areas of the 3 faces in mutually perpendicular planes equals the square of the area of the sloping face. A generalisation. . . .