Question

X
T
10.5 cm
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-shaped region.


Help me asap​

Answer 1

Answer:

Given:

XLMT is a rectangle.

Also,

XL = 10. 5 cm

LM = 21cm

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

From the figure,

Sum of two diameters = LM

$d + \frac{d}{2} = 21 \\ 3d = 42 \\ d = 14$

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So,

Diameter of larger circle = 14 cm

Radius of larger circle = 7cm.

Diameter of smaller circle = 7 cm

Radius of smaller circle = 3.5 cm.

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Area of rectangle XLMT

= Length × Breadth

= XL × LM

= 21 × 10.5

= 220.5 cm²

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Area of semi circle = 1/2πr²

Now,

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

Area of smaller semi circle = 1/2 ( 22/7)(7/2)² = 77/4 = 19.25cm²

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Area 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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