The perimeter of a rhombus is 40 cm and one of its angles is \(60^\circ\). What is the area of the rhombus?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \(50\sqrt{3}\) cm2
All four sides of a rhombus are equal. The diagonal joining the two \(120^\circ\) corners splits a rhombus with a \(60^\circ\) angle into two equilateral triangles, and an equilateral triangle of side \(a\) has area \(\displaystyle\frac{\sqrt{3}}{4}a^2\).
Side \(=40\div4=10\) cm
Area of one equilateral triangle \(\displaystyle=\frac{\sqrt{3}}{4}\times10^2=25\sqrt{3}\) cm2
Area of the rhombus \(=2\times25\sqrt{3}=50\sqrt{3}\) cm2
