Given a rhombus, as shown on the right, with diagonals of length 2a and 2b, express the area and the side s in terms of a and b.
The area is made up of four right triangles with total area of 2ab.
To find an expression for s consider this figure where the four right triangles from the rhombus are assembled at the vertices of an auxiliary square of side length a + b.
The area of the auxiliary square is equal to the sum of the area of the rhombus (the four triangles) and the area of a square of side length s formed on the side of the rhombus.
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