A rhombus has each side 8 cm and one of its angles is 60°. Find its area in ${\text{cm}}^2$. Take √3 = 1.73.

The shorter diagonal of a rhombus with a 60° angle joins the ends of two 8 cm sides that meet at 60°, so it is itself 8 cm and it splits the rhombus into two equilateral triangles of side 8 cm. Each has area (√3/4) × $64=(1.73/4)\times 64=27.68{\text{cm}}^2$, so the rhombus = $2\times 27.68=55.36{\text{cm}}^2.(27.68{\text{cm}}^2$ is one of the two triangles only; $64{\text{cm}}^2$ treats the rhombus as a square of side 8, which needs 90° corners; $110.72{\text{cm}}^2$ doubles once too often.)