Question

Find the Area of ​​the Shaded Potion Figure 15.3​

Answer 1

Question:-

• A rectangule of length 14 cm and breadth 10 cm.

• A semi circle inscribed in a rectangule whose diameter is 14 cm.

• Diagram provided by the user who asked the question.

• Find the shaded region.

Answer:-

• Area of shaded region = Area of Rectangle - Area of semi circle.

• First, Area of Rectangle = l * b

• l * b = 14 * 10 = 140 cm²

• Now, Area of semi circle,

• As the semi circle stands on the length of Rectangle, it becomes the diameter of the semi circle.

• Diameter of semi circle = 14 cm

• Radius = d / 2 = 14 / 2 = 7 cm.

• Area of semi circle = 1/2 ( πr² )

• 1/2 * 22/7 * 7 * 7

• 1/2 * 22 * 7 { Denominator of 22/7 and 7 gets cancelled }

• 0.5 * 154

• 77 cm²

• Area of Shaded region = Area of Rectangle - Area of semi circle

• 140 cm² - 77 cm²

• 63 cm²

Conclusion:-

• Therefore, Area of Shaded region = 63 cm².

Formulas used:-

• Area of Rectangle = Length * breadth = l * b

• Area of semi circle = 1/2 ( π * r² )

Answer 2

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$\LARGE\mathfrak{\underline{\underline\textcolor{aqua}{✯\; Given :-}}}$

$\large\textsf{ }$

$\qquad\tt{:}\longrightarrow\large\textsf{Length of the Rectangle = 14cm }$

$\qquad\tt{:}\longrightarrow\large\textsf{Breadth of the rectangle = 10cm}$

$\qquad\tt{:}\longrightarrow\large\textsf{Diameter of the semi circle = 14cm}$

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$\LARGE\mathfrak{\underline{\underline\textcolor{aqua}{✯\; To \; \; Find :-}}}$

$\large\textsf{ }$

$\qquad\tt{:}\longrightarrow\large\textsf{Area of the shaded region = ? }$

$\large\textsf{ }$

$\LARGE\mathfrak{\underline{\underline\textcolor{aqua}{✯\; Formula :-}}}$

$\large\textsf{ }$

$\qquad\tt{:}\longrightarrow\boxed{\large\textsf{ {\large\textsf\textcolor{purple}{Area}}_{\large\textsf\textcolor{purple}{( \; Rectangle \; )}} = \large\textsf\textcolor{purple}{l × b} }}$

$\qquad\tt{:}\longrightarrow\boxed{\large\textsf{ {\large\textsf\textcolor{purple}{Area}}_{\large\textsf\textcolor{purple}{( \; Semi Circle \; )}} } \large\textsf\textcolor{purple}{ = \cfrac{\large\textsf\textcolor{purple}{1}}{\large\textsf\textcolor{purple}{2}} }\large\textsf\textcolor{purple}{× πr²}}$

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$\LARGE\mathfrak{\underline{\underline\textcolor{aqua}{✯\; How \; \; To \; \; Solve :-}}}$

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• First we need to Find the Area of the given rectangle.
• Then we find the Area of the Semi Circle.
• And then we subtract the Area of the Semi Circle from the Area of the rectangle.
• Then finally we would get the Area of the shaded area in the given figure.

$\large\textsf{ }$

$\LARGE\mathfrak{\underline{\underline\textcolor{aqua}{✯\; Solution :-}}}$

$\large\textsf{ }$

$\qquad\large\textsf{✯\; \; {\large\textsf{Area}}_{\large\textsf{( \; Rectangle \; )}} = \large\textsf{l × b} }\\\\\\\qquad\large\textsf{= 14 × 10}\\\\\\\boxed{\large\textsf{ {\large\textsf\textcolor{red}{Area}}_{\large\textsf\textcolor{red}{( \; Rectangle \; )}} \large\textsf\textcolor{red}{= 140 sq. cm} }}$

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• Radius = 1\2 Diameter = 1\2 × 14
• Radius = 7cm

$\large\textsf{ }$

$\qquad\large\textsf{✯ \; \; {\large\textsf{Area}}_{\large\textsf{( \; Semi Circle \; )}} } \large\textsf{ = \cfrac{\large\textsf{1}}{\large\textsf{2}} }\large\textsf{× π × r²}\\\\\\\qquad\large\textsf{ = \cfrac{\large\textsf{1}}{\large\textsf{2}} × \cfrac{\large\textsf{22}}{\large\textsf{7}} \large\textsf{×7 × 7}}\\\\\\\qquad\large\textsf{ = \cfrac{\large\textsf{1}}{\large\textsf{2}} × \cfrac{\large\textsf{22}}{\large\textsf{7}} \large\textsf{49}}\\\\\\\qquad\large\textsf{= 11 × 7}\\\\\\\qquad\boxed{\large\textsf{ {\large\textsf\textcolor{red}{Area}}_{\large\textsf\textcolor{red}{( \; Semi Circle \; )}} \large\textsf\textcolor{red}{= 77 sq.cm} }}$

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$\qquad\large\textsf{✯\; \; {\large\textsf{Area}}_{\large\textsf{( \; Shaded Area \; )}} = {\large\textsf{Area}}_{\large\textsf{( \; Rectangle \; )}} - {\large\textsf{Area}}_{\large\textsf{( \; Semi Circle \; )}} }\\\\\\\qquad\large\textsf{= 140 - 77}\\\\\\\qquad\boxed{\large\textsf{ {\large\textsf\textcolor{red}{Area}}_{\large\textsf\textcolor{red}{( \; Shaded Area \; )}} \large\textsf\textcolor{red}{= 63 sq.cm} }}$

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$\large\textsf{ }$

∴ Area of the Shaded Area = 63 cm².

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