Correct Answer - Option 2 : ¼ square unit
Given:
Perimeter of a rhombus = 2cot θ
Sum of diagonals = cosec θ
Formula used:
(d1)2 + (d2)2 = 4a2
Here,
d1 and d2 are diagonals of rhombus
a is the side of rhombus
Calculation:
Perimeter of a rhombus = 2 cot θ
⇒ 4a = 2cot θ
⇒ cot θ = 2a
⇒ d1 + d2 = cosec θ
⇒ (d1)2 + (d2)2 + 2d1d2 = cosec2 θ
⇒ 4a2 + 2d1d2 = cosec2 θ
⇒ cot2 θ + 2d1d2 = cosec2 θ
⇒ d1d2 = ½
⇒ Area of rhombus = (½) d1d2
⇒ Area of rhombus = (½)(½) = ¼ square unite
∴ Area of rhombus is ¼ square unite.