Diagonals of Length

Given a rhombus, as shown on the right, with diagonals of length2aand2b, express the area and the side s in terms ofaandb.

The area is made up of four right triangles with total area of.2ab

To find an expression forsconsider this figure where the four right triangles from the rhombus are assembled at the vertices of an auxiliary square of side lengtha + 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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