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One diagonal of a rhombus is 25% more than the other diagonal. The area of the rhombus is 40 cm2. A circle is drew starting from one of the vertices of the rhombus in such a way that the rhombus is completely inside the circle. What is the area of such a circle?

One diagonal of a rhombus is 25% more than the other diagonal. The area of the rhombus is 40 cm2. A circle is drew starting from one of the vertices of the rhombus in such a way that the rhombus is completely inside the circle. What is the area of such a circle? Correct Answer 25π cm<span style="position: relative; line-height: 0; vertical-align: baseline; top: -0.5em;font-size:10.5px;">2</span>

Given:

One diagonal of a rhombus is 25% more than the other diagonal. The area of the rhombus is 40 cm2. 

Formula used:

Area of the rhombus = (1/2) × d1 × d2

Area of circle = π d2/4

Calculations:

Let d be the smaller diagonal, then the longer diagonal will be 1.25d.

Area of the rhombus = (1/2) × d1 × d2

⇒ (1/2) × d × 1.25d = 0.625d2

⇒ 0.625d2 = 40

⇒ d = 8 cm

The longer diagonal will be the diameter of the circle,

Area of circle = (π (1.25d)2)/4

⇒ 100π/4 = 25π cm2

Additional Information

Rhombus is special types of parallelogram in which all sides are equal.

Area of rhombus = 0.5 × (product of the lengths of the diagonals)

Area of rhombus = (side length of a rhombus)2 × sin of any interior angle.

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