Question

In the above figure, 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.​

Answer 1

Explanation:

Answer : Area of non shaded region is 124.25cm²

Given,

XLMT is a rectangle.

Also,

XL = 10. 5 cm

LM = 21cm

Diameter of smaller circle is half the diameter of larger circle ( Given)

Diameter of smaller circle is half the diameter of larger circle ( Given)Let the diameter of larger circle = d ( Assumption)

Diameter of smaller circle is half the diameter of larger circle ( Given)Let the diameter of larger circle = d ( Assumption)Then, Diameter of smaller circle = d/2

Diameter of smaller circle is half the diameter of larger circle ( Given)Let the diameter of larger circle = d ( Assumption)Then, Diameter of smaller circle = d/2From the figure,

Diameter of smaller circle is half the diameter of larger circle ( Given)Let the diameter of larger circle = d ( Assumption)Then, Diameter of smaller circle = d/2From the figure,Sum of two diameters = LM

\begin{lgathered}d + \frac{d}{2} = 21 \\ \\ 3d = 42 \\ \\ d = 14\end{lgathered}

d+

2

d

=21

3d=42

d=14

So,

So,Diameter of larger circle = 14 cm

So,Diameter of larger circle = 14 cmRadius of larger circle = 7cm.

So,Diameter of larger circle = 14 cmRadius of larger circle = 7cm.Diameter of smaller circle = 7 cm

So,Diameter of larger circle = 14 cmRadius of larger circle = 7cm.Diameter of smaller circle = 7 cmRadius of smaller circle = 3.5 cm.

So,Diameter of larger circle = 14 cmRadius of larger circle = 7cm.Diameter of smaller circle = 7 cmRadius of smaller circle = 3.5 cm.Area of rectangle XLMT

So,Diameter of larger circle = 14 cmRadius of larger circle = 7cm.Diameter of smaller circle = 7 cmRadius of smaller circle = 3.5 cm.Area of rectangle XLMT= Length × Breadth

So,Diameter of larger circle = 14 cmRadius of larger circle = 7cm.Diameter of smaller circle = 7 cmRadius of smaller circle = 3.5 cm.Area of rectangle XLMT= Length × Breadth= XL × LM

So,Diameter of larger circle = 14 cmRadius of larger circle = 7cm.Diameter of smaller circle = 7 cmRadius of smaller circle = 3.5 cm.Area of rectangle XLMT= Length × Breadth= XL × LM= 21 × 10.5

So,Diameter of larger circle = 14 cmRadius of larger circle = 7cm.Diameter of smaller circle = 7 cmRadius of smaller circle = 3.5 cm.Area of rectangle XLMT= Length × Breadth= XL × LM= 21 × 10.5= 220.5 cm²

Area of semi circle = 1/2πr²

Area of semi circle = 1/2πr²Now,

Area of semi circle = 1/2πr²Now,Area of larger semi circle = 1/2 ( 22/7) ( 7²) = 11 ( 7) = 77cm²

Area of semi circle = 1/2πr²Now,Area of larger semi circle = 1/2 ( 22/7) ( 7²) = 11 ( 7) = 77cm²Area of smaller semi circle = 1/2 ( 22/7)(7/2)² = 77/4 = 19.25cm²

Area of semi circle = 1/2πr²Now,Area of larger semi circle = 1/2 ( 22/7) ( 7²) = 11 ( 7) = 77cm²Area of smaller semi circle = 1/2 ( 22/7)(7/2)² = 77/4 = 19.25cm²Area of unshaded region = Area of rectangle XLMT - Area of two semi circles

Area of semi circle = 1/2πr²Now,Area of larger semi circle = 1/2 ( 22/7) ( 7²) = 11 ( 7) = 77cm²Area of smaller semi circle = 1/2 ( 22/7)(7/2)² = 77/4 = 19.25cm²Area of unshaded region = Area of rectangle XLMT - Area of two semi circles= 220.5 - 77 - 19. 25

Area of semi circle = 1/2πr²Now,Area of larger semi circle = 1/2 ( 22/7) ( 7²) = 11 ( 7) = 77cm²Area of smaller semi circle = 1/2 ( 22/7)(7/2)² = 77/4 = 19.25cm²Area of unshaded region = Area of rectangle XLMT - Area of two semi circles= 220.5 - 77 - 19. 25= 124.25 cm²

Therefore, Area of unshaded region is 124.25cm²

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