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Question:

Three semicircles each of diameter 3 cm, a circle of diameter 4.5 cm and a semicircle of radius 4.5 cm are drawn in the given figure. Find the area of the shaded region.

Solution:

Area of big semicircle=1/2πr²=π/2×(4.5)²
Area of one small semicircle=π/2×(1.5)²
Area of the given figure=π/2[(4.5×4.5)/100+(1.5×1.5)/100]=45π/4 cm²
Area of circle=π×(4.5/2)²
Area of the shaded region=Area of a given figure - Area of circle
Area of small semicircles=45π/4 - π/4(4.5)²×4=45π/4 - 45π/4 =0
Area of the shaded region = Area of big semicircle - Area of circle - Area of 3 small semicircles
= (π/2)(4.5)² - π(4.5/2)² - 3(π/2)(1.5)²
= (π/2)(20.25) - π(5.0625) - 3(π/2)(2.25)
= 10.125π - 5.0625π - 3.375π
= 1.6875π
= 1.6875 × 22/7
≈ 5.30 cm²