Radius of sector 14 cm
Area of sector
= 90°/360° × πr² = 1/4 × πr²
= 1/4 × 22/7 × 14 × 14 = 154 cm²
In AABC,
BC² AC² + AB² ⇒ BC² = (14)² + (14)² ⇒ BC² = 196 + 196
⇒ BC² = 39² ⇒ BC = √392 ⇒ BC = 14√2
Therefore, the diameter of semicircle = BC = 14√2
Radius of semicircle = 7√2 cm
Area of semicircle
= 1/2 × πr² = 1/2 × π(7√2)² = 1/2 × 22/7 × 7√2 × 7√2 = 154 cm²
Area of triangle ABC
= 1/2 × AB × BC = 1/2 × 14 × 14 = 98 cm²
Area of shaded region
= Aera of triangle ABC + Area of semicircle – Area of quadrant
= (98 + 154 – 154) cm²
= 98 cm²