Question

A square OPQR is inscribed in a quadrant OAQB of a ciricle. If the radius of circle is 6√2 cm, Find the area of shaded region​

Answer 1

Answer:

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Step-by-step explanation:

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Answer 2

Area of shaded region is 20.57 cm²

Step-by-step explanation:

• Given data

        Radius of circle (R) = 6√2 cm = Diagonal of square (d)

        R² = (6√2)² = 72

• Here R represent radius of circle

       d represent diagonal of square

• We know area of quadrant circle which are given below

        $\mathbf{area OAQB =\frac{\pi\times R^{2}}{4}}$        ...1)

• We also know area of square in terms of diagonal

        $\mathbf{area OPQR =\frac{1}{2}\times d^{2}}$    

        Put diagonal (d) = Radius (R) in above equation

        $\mathbf{area OPQR =\frac{1}{2}\times R^{2}}$       ...2)

• Now

• Area of shaded region = Area of quadrant circle - Area of square

        $\mathbf{Area\ of\ shaded\ region =\frac{\pi \times R^{2}}{4}-\frac{1}{2}\times R^{2}}$

        $\mathbf{Area\ of\ shaded\ region =\frac{22 \times 72}{7\times 4}-\frac{1}{2}\times 72}$

        Area of shaded region = 20.57 cm²