In the figure, `square XLMT` is a rectangle. `angle M=21 cm`, XL = 10. 5 cm. Diamter of the smaller semicircle is half the diameter of larger semicircle. Find the area of non-shaded region.

Explanation

Let, diameter of smaller semicircle = 2r
Diameter of larger semicircle = 4r
Now LM = 21 cm `" "…("Given")`
`thereforeLM=2r+4r`
`therefore 21=6r`
`thereforer=(21)/6" thereforer=3.5cm`
`therefore` Radius of a smaller semicircle = r = 3.5 cm
and radius of larger semicircle (R) = `2xx3.5=7cm`
Now area of smaller semicircle `= 1/2pir^2`
`=1/2xx(22)/7xx3.5xx3.5`
`=19.25 cm^2`
Area of larger semicircle `=1/2piR^2`
`=1/2xx(22)/7xx7xx7`
`=77cm^2`
Now area of rectangle `=lxxb`
`=21xx10.5`
`=220.5 cm^2`
`therefore` Area of non-shaded region = Area of rectangle - (Area of smaller semicircle + Area of larger semicircle)
= 2220.50 - (19.25 + 77)
`=220.50 - 96.25
`=124.25 cm^2`
Area of non-shaded region is `124.25 cm^2`