In the given figure, a square ABCD is inscribed in a quadrant APCQ. If AB = 16 cm, find the area of the shaded region (take $\pi$ = 3.14) correct to two places of decimal.

145.92 cm²

We know that,

Area of a square = (side)²

Area of a quadrant of a circle = \(\frac{1}{4}\) πr²

The diagonal of a square = a\(\sqrt {2}\)

We have,

AB = 16 cm

then,

AC = 16\(\sqrt {2}\)

Area of the shaded region = Area of the quadrant - the area of the square

= Area of the shaded region = π × (16\(\sqrt {2}\))²/4 - 16²

= 3.14 × 128 – 256 = 401.92 – 256 = 145.92 cm²