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# Take a Square

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### Compare Areas

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### Diagonal Touch

Links to the University of Cambridge website
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Nurturing young mathematicians: teacher webinars

30 April (Primary), 1 May (Secondary)

30 April (Primary), 1 May (Secondary)

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Age 14 to 16

Challenge Level

Cut off three congruent right angled isosceles triangles to produce a pentagon.

With two lines, cut the pentagon into three parts which can be rearranged into another square.

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

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.

Weekly Problem 21 - 2012

Two rectangles are drawn in a rectangle. What fraction of the rectangle is shaded?