Question

find the area of shaded region and
the length of arc AB​

Answer 1

ANS

Area of shaded = $\boxed{ \bf\red{ 76.93 cm² }}$

Arc AB = $\boxed{ \bf\red{21.98cm}}$

Consider OAB

• it is $\bf\frac{1}{4}$ of circle

• Radius = 14 cm

• Area of circle = πr²

• Area of OAB = $\bf\frac{1}{4} π 14²$

• Area Of OAB = 153.86 cm²

$\rule{10cm}{0.05cm}$

CONSIDER OB ,

• It is $\bf\frac{1}{2}$ of circle

• Radius = 7 cm

• Area Of OB = $\bf\frac{1}{2} π 7²$

• area of OB = 76.93 cm²

$\rule{10cm}{0.05cm}$

Area of shaded part

• $\bf A_{Shaded}$ = $\bf A_{OAB} - \: A_{OB}$

• $\bf A_{Shaded}$ = 153.86 - 76.93

• $\bf A_{Shaded}$ = 76.93 cm²

$\rule{10cm}{0.05cm}$

ARC AB

• since it is $\bf\frac{1}{4}$ of circle

• Circumference = $\bf\frac{2πr}{4}$

• Circumference = $\bf\frac{2π14}{4}$

• Circumference = 21.98 cm

$\rule{10cm}{0.05cm}$