Question

Two semicircles have been drawn
inside the square ABCD of side 14 cm. Find the area of the shaded region as well as theunshaded region.​

Answer 1

Step-by-step explanation:

Square

solve for area

A=196cm²

a Side

14cm

Solution

A=a2=142=196cm²

hope its help you..

Answer 2

$\LARGE{\color{royalblue}{\textsf{\textbf{ Qυєѕтiση }}}}$

• Two semicircles have been drawn inside the square ABCD of side 14 cm. Find the area of the shaded region as well as the unshaded region.

$\LARGE{\color{royalblue}{\textsf{\textbf{ αnѕwєr }}}}$

• Using this formula

$\boxed{ \red{ \sf \: Area \: of \: shaded \: region= Area \: of \: square \: ABCD \sf- Area \: of \: semicircle \: APD - Area \: of \: semicircle \: BPC}}$

Area of square ABCD

• Side of square = 14 cm

$\sf \: Area \: of \: square = Side \times Side \\ \\ \sf \: = 14 \times 14 \\ \\ \sf \: = 196 \: cm²$

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Area of semi circle APD

• Diameter = AD = 14 cm
• So, radius= 7 cm

$\sf \: Area \: of \: semicircle \: APD = \frac{1}{2}\pi r² \\ \\ \sf = \frac{1}{2} \times \frac{22}{7} \times {(7)}^{2} \\ \\ \sf \: =\frac{22}{7} \times 7×7 \\ \\ = \sf 77 \: cm²$

Similarly,

For semicircle BPC

• Diameter BC = 14 cm
• Since diameter is same

Area of semi circle BPC = Area of semi circle APD = 77 cm²

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Now,

$\sf \: Area \: of \: shaded \: region= Area \: of \: square- Area \: of semicircle \: APB- Area \: of \: semicircle \: BPC$

$\sf= 196-77-77 \\ \\ \sf = 196-(77+77) \\ \\ \sf= 196 - (154) \\ \\ = \boxed{ \red{\sf42 \: cm²}} \pink \bigstar$

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$\therefore \sf \: Hence, area \: of \: shaded \: region \: \bold {42 cm²}$ㅤㅤ

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$\sf \: Area \: of \: unshaded \: region = Area \: of \: two \: semicircles \\ \\ = \boxed{ \red{\sf \: 154 \: cm².}} \pink \bigstar$

$\therefore \sf \: Hence, \: Area \: of \: unshaded \: region \: \bold{154 \: cm².}$

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