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In figure , rectangle $ABCD$ is inscribed in a circle. If the radius of the circle is $2 units$ and $CD = 2 units$ . What is the area of the shaded region?

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0.362 sq. units

0.62 sq. units

0.32 sq. units

0.36 sq. units

answer is A.

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Detailed Solution

Given,

CD = 2 units = AB

and radius is

2

units.

Area of an equilateral triangle is

\frac{\sqrt{3}}{4} a^{2}

.
Let

O

be the centre of the circle.
Area of shaded region

=

Area of sector made by arc

AB

with centre - area of triangle

AOB

Area of shaded region

= \frac{Length of arc CD}{2 πr} \times πr - \frac{\sqrt{3}}{4} a^{2}

\Rightarrow

Area of shaded region

=

\frac{2}{2 π \times 2} \times \frac{22}{7} \times 2 \times 2 - \frac{1}{2} \times 2 \times 2 \times \frac{\sqrt{3}}{2}

\Rightarrow

Area of shaded region

= \frac{88}{42} - \sqrt{3}

\Rightarrow

Area of shaded region

= 2.095 - 1.732

\Rightarrow

Area of shaded region

= 0.362

sq. units
Hence, option 1 is correct.

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In figure , rectangle ABCD is inscribed in a circle. If the radius of the circle is 2 units and CD=2 units. What is the area of the shaded region?

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In figure , rectangle $ABCD$ is inscribed in a circle. If the radius of the circle is $2 units$ and $CD = 2 units$ . What is the area of the shaded region?