Question

AD is the diameter of a circle of radius 6 cm and AB=BC=CD. Semi-circles are drawn with AB and BD as diameters as shown in the figure.Find the perimeter and area of the shaded region.

Answer 1

Answer:

Step-by-step explanation:

Given AD = 6 cm

Also given that AB = BC = CD

=> AB = 2 cm

    BD =4 cm

1) Perimeter of the shaded region is equal to Sum of perimeter of semicircular arc AD + Perimeter of semicircular arc AB + Perimeter of semicircular arc BD

perimeter of semicircular arc AD = π*3 = 3π

perimeter of semicircular arc AB = π*1 = π

perimeter of semicircular arc BD = π*2 = 2π

Perimeter of shaded region = 3π + π + 2π

=6π cm

2) Area of shaded region = Area of semicircular region AB +Area of semicircular region AD - Area of semicircular region BD

Area of semicircular region AB = π*1²/2 = π/2

Area of semicircular region AD = π*3²/2 = 9π/2

Area of semicircular region BD = π*2²/2 = 2π,

Thus Area of shaded region = π/2 + 9π/2 -2π

= 3π cm²