A doorway is decorated as shown in the adjoining fig .there are four semicircles BC the diameter of the larger semicircle is of length 84cm the centres of the three equal semicircles lie on BC .ABC is an isosceles triangle with AB =AC
Answers
1932 cm² is the area of the shaded region
Step-by-step explanation:
Complete Question : see attached figure
find area of shaded region
Diameter of Larger Semicircle = 84 cm
Radius = 84/2 = 42 cm
Area of Larger Semi circle = (1/2) π * (42)²
π = 22/7
= (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) * (14)²
= 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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Answer:
1932 cm2
Step-by-step explanation:
it is very helpful
