Question

Find the area of the shaded region. Here ABC is a right-angled
triangle where AB = 8 cm, BC = 6 cm and ADC, BEC and AFB are
semicircles.
​

Answer 1

Solution :

In ∆ ABC

→ AB² + BC² = AC²

→ 8² + 6² = AC²

→ AC² = 64 + 36

→ AC = √100

→ AC = 10 cm

Area of ∆ ABC

⇒ Area = 1/2 × Base × Height

⇒ Area = 1/2 × 6 × 8

⇒ Area = 3 × 8

⇒ Area = 24 cm²

Area of BEC

⇒ Area = 1/2 × πr²

⇒ Area = 1/2 × 3.14 × 3 × 3

⇒ Area = 1/2 × 28.26

⇒ Area = 14.13 cm²

Area of AFB

⇒ Area = 1/2 × πr²

⇒ Area = 1/2 × 3.14 × 4 × 4

⇒ Area = 1/2 × 50.24

⇒ Area = 25.12 cm²

Area of ADC

⇒ Area = 1/2 × πr²

⇒ Area = 1/2 × 3.14 × 5 × 5

⇒ Area = 1/2 × 78.5

⇒ Area = 39.25 cm²

Area of shaded region

→ 24 + 14.13 + 25.12 + 39.25

→ 102.5 cm²