Question

The radius of circle is 14 cm what is the area sagment whose arc is measure 90

Answer 1

$\large{\boxed{ \bf{SOLUTION }}}$

Radius of circle = 14 cm

Angle of sector = 90°

$\bf{AREA \: OF \: SECTOR = \pi {r}^{2} \frac{ \theta}{360} }$

$= \frac{22}{7} \times 14 \times 14 \times \frac{90}{360} \\ \\ 22 \times 7 = 157 {cm}^{2}$

$A.O.S= \frac{22}{7} \times 14 \times 14 \times \frac{90}{360} \\ \\A.O.S = 22 \times 7 = 157 {cm}^{2}$

Now find the area of right triangle whose side are 14 cm :

$\bf{AREA \: OF \: \triangle = \frac{1}{2} \times b \times h} \\ \\ AREA = \frac{1}{2} \times 14 \times 14 \\ \\ AREA = 98 {cm}^{2}$

Area of segment :

Area of sector – Area of triangles

$\large \boxed{ \bf{ Area = 157 - 98 = 59 {cm}^{2} } }$