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Compare Areas

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

Semi-detached

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.

Diagonal Touch

Weekly Problem 21 - 2012
Two rectangles are drawn in a rectangle. What fraction of the rectangle is shaded?

Take a Square

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.

A square with three isosceles triangles removed from three corners to form a pentagon
The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice.
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