Exploring areas of rectangles, triangles, parallelograms and trapeziums including some ignored aspects. Models can be made using stiff paper/card/boxes.

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Elegant proofs of mathematical statements present the beauty of mathematics and enhance our learning pleasure. This is particularly so for ‘proofs without words’ which significantly improve the visual proof capability. In this article, we present three largely visual proofs which carry a great deal of elegance. In a strict sense they are not pure proofs without words because of the mathematical expressions and formulas that appear in them. Nevertheless, they carry a lot of appeal.

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