Question

answer this.............

Answer 1

Let's say the largest semicircle with diameter(D) 14cm is T

semicircles with diameter(d) 3.5cm as X and Y

semicircle with diameter(d') 7cm as Z
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Length of Boundary = arc length of T + arc length of X + arc length of Z + arc length of Y

= πD/2 + πd/2 + πd'/2 + πd/2

= π/2 ( D + d + d' + d)

= π/2 ( 14 + 3.5 + 3.5 + 7)

= π/2 ( 28 )

= 22/7 × 1/2 × 28

= 44cm

So length of boundary is 44cm.
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Use the formula: Area of semicircle = 1/2 × πr^2 = 1/2 × π(D/2)^2 = 1/2 × πD^2/4 = (πD^2)/8

=> area of semicircle = (π/8) × D^2

Area of shaded region = Area of semicircle T - area of semicircle X - area of semicircle Y + area of semicircle Z

= (π/8) × 14^2 - (π/8) × 3.5^2 - (π/8) × 3.5^2 + (π/8) × 7^2

= (π/8) × [ 14^2 - 3.5^2 - 3.5^2 + 7^2]

= (π/8) × [ 196 - 12.25 - 12.25 + 49]

= (π/8) × (196 - 24.5 + 49)

= (π/8) × 220.5

= 22/7 × 1/8 × 220.5

= 22/8 × 220.5/7

= 11/4 × 31.5

= 346.5/4

= 86.625 cm^2

Area of shaded region is 86.625 cm^2