Question

find its area and perimeter (of the shaded region)
all measures are in CM ​

Answer 1

$\large{\mathfrak{\underline{\underline{Answer:-}}}}$

• Area = 50.75 cm²

• Perimeter = 23cm

${\mathfrak{\underline{\underline{Step-By-Step-Explanation:-}}}}$

$\rule{200}{2}$

⇒ Area

$\sf{Area \: of \: Figure \: = \: A_{F}}$

$\sf{Area \: of \: Rectangle \: = \: A_{R}}$

$\sf{Area \: of \: Semicircle \: = \: A_{S}}$

_______________________

Area of rectangle = l × b

= 7 × 10

⇒ 70 cm²

$\bf{A_{R} \: = \: 70cm}$

_____________________________

Diameter = 7cm

Radius = 7/2 ⇒ 3.5 cm

Area of Semicircle = πr²/2

⇒ π × 12.25 /2

⇒ 12.25 × 22/7× 2

⇒ 269.5/14

⇒ 19.25 cm²

$\bf{A_{S} \: = \: 19.25cm^{2}}$

________________________

______________

Area of figure

$\bf{A_{F} \: = \: A_{R} \: - \: A_{S}}$

_________________[Put Values]

Area of Figure = 70 - 19.25

Area of Figure = 50.75cm²

$\large{\sf{\boxed{\boxed{A_{F} \: = \: 50.75cm^{2}}}}}$

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⇒ Perimeter

$\sf{Perimeter \: of \: Figure \: = \: P_{F}}$

$\sf{Perimeter \: of \: Rectangle \: = \: P_{R}}$

$\sf{Perimeter \: of \: Semicircle \: = \: P_{S}}$

_______________________

Perimeter of Rectangle = 2(l+b)

⇒ 2(10+7)

⇒ 2(17)

⇒ 34cm

$\bf{P_{R} \: = \: 34cm}$

_________________________

Perimeter of Semicircle = πr

⇒ 22 × 3.5/7

⇒ 11cm

$\bf{P_{S} \: = \: 11cm}$

_______________________

________________

Perimeter of Figure

$\bf{P_{F} \: = \: P_{R} \: - \: P_{S}}$

_____________[Put Values]

⇒ 34 - 11

⇒ 23cm

$\large{\sf{\boxed{\boxed{P_{F} \: = \: 23cm}}}}$