A doorway is decorated as shown in the figure. There
are four semi-circles. BC, the diameter of the larger
semi-circle is of length 84 cm. Centres of the three
equal semi-circles lie on BC. ABC is an isosceles
triangle with AB = AC. If BO = OC, find the area of
the shaded region.**
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Answers
1932 cm² is the area of the shaded region
Step-by-step explanation:
Diameter of Larger Semicircle = 84 cm
Radius = 84/2 = 42 cm
Area of Larger Semi circle = (1/2) π 42²
= (1/2) (22/7) * 42²
= 2772 cm²
Radius of Small circle = 42/3 = 14 cm
Area of 3 Small Semi circle = 3 (1/2) (22/7) * 14²
= 924 cm²
ABC is an isosceles triangle with AB = AC
=> AO ⊥ BC
AO = 42 cm radius
Area of Δ ABC = (1/2) * 84 * 42
= 1764 cm²
area of the shaded region = Area of Larger Semi circle + Area of 3 Small Semi circle - Area of Δ ABC
= 2772 + 924 - 1764
= 1932 cm²
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