Question

(6) The figure shows a rectangle and 6 identical semicircles in a circle. Find the area of the shaded part. (Take π = 3.14.)​

Answer 1

`\blue{\boxed{\bold{\mathbb{SOLUTION}}}}`

Area of the biggest circle:

`\pi r^(2)=\pi * 6^(2)=\pi * 36 \ cm^2`.

Area of the rectangle:

`4 * (2+2+2+2) = 4 * 8 = 32 \ cm^2`.

Area of the 6 semicircles:

`6 * (1)/(2) * \pi * r^2 = 3 * \pi * 2^2 = \pi * 12 \ cm^2.`

Total shaded area:

Biggest circle area - rectangle area - 6 semicircles area

`= \pi * 36 - 32 - \pi * 12\\= \pi * (36-12) - 32\\= \pi * 24 - 32\\= 3.14 * 24 - 32\\= 75.36 - 32\\= \boxed{43.36 \ cm^2}`

Therefore, the shaded part area is
`43.36 \ cm^2`.

`\aqua{\boxed{\mathfrak{Thank \: You}}}\\\aqua{\boxed{\bold{answered \: by: \: akbarsdtazm}}}`