Question

In the given figure, OABC is a square of side 14 cm. Taking π = `22/7` the area of the shaded portion is:

Options

• 154 cm²

• 196 cm²

• 42 cm²

• 52 cm²

Answer 1

42 cm²

Explanation:

The square has a side length of 14 cm, giving a total area of \[14 \times 14 = 196\text{ cm}^2\]. The unshaded region is a quadrant of a circle with a radius of $14\text{ cm}$:

\[\text{Area of quadrant} = \frac{1}{4} \pi r^2 = \frac{1}{4} \times \frac{22}{7} \times 14^2 = 154\text{ cm}^2\]

Subtracting this from the area of the square gives the shaded portion: \[196 - 154 = 42\text{ cm}^2\].