Question

Find an expression for the area of the shaded region? Now let r= 4 cm, calculate the area?

Answer 1

`2r^2(8 - π)` and `"155.47 cm"^2`

Explanation:

From diagram we can say
There is a square (of side length `4r`), a semicircle (of radius `2r`) and 4 circles (of radius `r` each)

• Area of square`= (4r)^2 = 16r^2`
• Area of semicircle`= (π(2r)^2)/2 = 2pir^2`
• Area of circle`= pir^2`

Area of shaded region is

`A = 2pir^2 + 16r^2 - 4(pir^2)`

`A = 16r^2 - 2pir^2`

`color(blue)(A = 2r^2(8 - π))`

Now, if `r = 4\ "cm"`

`A = 2(4\ "cm")^2(8 - π) = "155.47 cm"^2`