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.
Answer & explanation
Correct answer: option 4
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