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In the given figure, OABC is a square of side 14 cm. Taking π=227π = \dfrac{22}{7}, the area of the shaded portion is :

In the given figure, OABC is a square of side 14 cm. Taking π = 22/7, the area of the shaded portion is : Area and Perimeter of Plane Figures, Concise Mathematics Solutions ICSE Class 9.
  1. 154 cm2

  2. 196 cm2

  3. 42 cm2

  4. 52 cm2

Mensuration

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Answer

Side of the square = Radius of the circle = 14 cm

Area of shaded portion = Area of square - 14\dfrac{1}{4} Area of quarter circle

=Side214πr2=14214×227×142=1962228×14×14=196222×14=1963082=196154=42cm2= Side^2 - \dfrac{1}{4} πr^2\\[1em] = 14^2 - \dfrac{1}{4} \times \dfrac{22}{7} \times 14^2\\[1em] = 196 - \dfrac{22}{28}\times 14 \times 14\\[1em] = 196 - \dfrac{22}{2} \times 14\\[1em] = 196 - \dfrac{308}{2} \\[1em] = 196 - 154\\[1em] = 42\text{cm}^2

The area of the shaded portion is 42 cm2.

Hence, option 3 is the correct option.

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