Find the perimeter and area of the shaded region shown in the figure. The four corners are circle quadrants and at the centre, there is a circle.

4 quadrants = 1 full circle

Circumference of circle = 2πr

= 2 × 3.14 × 1

= 6.28 cm.

Length of each shaded straight sides = 4 - 1 - 1 = 2 cm.

Total length = 4 × 2 = 8 cm.

Central circle boundary :

radius = $\dfrac{2}{2}$ = 1 cm.

Circumference of circle = 2πr

= 2 × 3.14 × 1

= 6.28 cm.

Total perimeter = 6.28 + 8 + 6.28 = 20.56 cm.

Area of shaded region = Area of the square - (Area removed at the corners - Area of central circle)

Area of square = (side)² = 4² = 16 cm².

Area removed at the corners :

Area of 1 quadrant = $\dfrac{1}{4}$ πr²

= $\dfrac{1}{4}$ × 3.14 × 1² = 0.785

∴ For 4 quadrants = 4 × 0.785 = 3.14 cm².

Area of central circle = πr²

= 3.14 × 1² = 3.14 cm².

Area of shaded region = Area of square - Area of central circle - Area of 4 quadrants

= 4 × 4 - (3.14 + 3.14)

= 16 - 6.28 = 9.72 cm².

Hence, perimeter = 20.56 cm and area of shaded region = 9.72 cm².