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Broad Topics >

Measuring and calculating with units > Area - squares and rectangles

##### Age 16 to 18 Challenge Level:

Follow the hints and prove Pick's Theorem.

##### Age 16 to 18 Challenge Level:

Change the squares in this diagram and spot the property that stays
the same for the triangles. Explain...

##### Age 16 to 18 Challenge Level:

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.

##### Age 14 to 16 Challenge Level:

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.

##### Age 16 to 18 Challenge Level:

Find a quadratic formula which generalises Pick's Theorem.

##### Age 14 to 16 Challenge Level:

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

##### Age 16 to 18 Challenge Level:

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. . . .

##### Age 14 to 16 Challenge Level:

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.