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प्रश्न
In the above figure, `square`XLMT is a rectangle. LM = 21 cm, XL = 10.5 cm. Diameter of the smaller semicircle is half the diameter of the larger semicircle. Find the area of non-shaded region.
उत्तर
Given: `square`XLMT is a rectangle.
LM = XT and XL = TM .....(Opposite sides are equal)
∴ XT = 21 cm
TM = 10.5 cm
To find the area of a non-shaded region
The diameter of a smaller semicircle is half the diameter of a larger semi-circle.
Let the diameter of the larger semicircle is D and the diameter of the smaller semicircle be `1/2 xx D = D/2`.
Now, the diameter of the smaller semicircle + the diameter of the larger semicircle = 21 cm
`D + D/2 = 21`
`(2D + D)/2 = 21`
`(3D)/2 = 21`
`3D = 21 xx 2`
`D = (21 xx 2)/3`
D = 14
A(smaller semi-circle) = `1/2 pir^2`
= `1/2 xx 22/7 xx 7/2 xx 7/2`
= `77/4 "cm"^2`
A(largerer semi-circle) = `1/2pir^2`
`= 1/2 xx 22/7 xx 14/2 xx 14/2`
= `77 "cm"^2`
A(`square`XLMT) = length × breadth
= LM × XL
= 21 cm × 10.5 cm
= 220.5 cm2
Area of the non-shaded region
= A(`square`XLMT) – A(smaller semi-circle) – A(larger semi-circle)
= 220.5 – `77/4 - 77`
= 220.5 – 19.25 – 77
= 124.25 cm2
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