The perimeter of a rhombus is 48 cm and one of its angles is \(60^\circ\). What is the area of the rhombus?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \(72\sqrt{3}\) cm2
All sides of a rhombus are equal, so the shorter diagonal cuts a rhombus with a \(60^\circ\) angle into two equilateral triangles, each of area \(\frac{\sqrt{3}}{4}a^2\).
Side \(=48\div4=12\) cm
Two sides of 12 cm with a \(60^\circ\) angle between them close an equilateral triangle of side 12 cm
One triangle \(=\displaystyle\frac{\sqrt{3}}{4}\times12^2=36\sqrt{3}\) cm2
Rhombus \(=2\times36\sqrt{3}=72\sqrt{3}\) cm2
