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If perimeter of a rhombus is 2 cot θ and sum of diagonals is cosec θ. Find the area of rhombus.
1. 1 square unit
2. ¼ square unit
3. 4 square unit
4. 1/9 square unite

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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.

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