AC and BD are two perpendicular diameters of a circle with centre O. If AC = 16 cm, calculate the area and perimeter of the shaded part.

Given,

AC = 16 cm (diameter)

Radius (r) = $\dfrac{16}{2}$ = 8 cm.

Two perpendicular diameters divide the circle into 4 quadrants.

Area of each quadrant = $\dfrac{1}{4}$ Area of circle

Since, 2 quadrants are shaded. Thus,

$\therefore \text{Area of shaded part} = 2 \times \dfrac{4}{2} πr^2 \\[1em] = \dfrac{1}{2} \times 3.14 \times 8^2 \\[1em] = \dfrac{1}{2} \times 3.14 \times 64 \\[1em] = 3.14 \times 32 \\[1em] = 100.48 \text{ cm}^2.$

Full circumference = 2πr = 2 × 3.14 × 8 = 50.24 cm.

Only quarter arc is shaded.

AD = $\dfrac{1}{4}$ × 50.24 = 12.56.

Perimeter of the shaded part = 2(OA + OD + arc AD)

Perimeter = 2(8 + 8 + 12.56)

= 2(16 + 12.56)

= 2(28.56) = 57.12 cm.

Hence, area = 100.48 cm² and perimeter = 57.12 cm.