Question

the perimeter of sector of a circle of area 25 square centimetre is 20 cm find area of sector

Answer 1

Area of the circle= 2*pi*r= 25*pi
r=25/2 cm

Perimeter of the sector = 2*l/r=20
2*l/(25/2)=20
l=125cm

Area = r*l*/2
(25/2*125)/2=3125/4=781.25cm ^2

Answer 2

Area of circle = pi ×r^2

25pi = pi × r^2

$r = \sqrt{25} = 5cm$

P of sector = 2r + r × theta

20 = 2 × 5 + 5 theta

20. - 10 = 5 theta

10 / 5 = 2= theta

Now area of sector = (theta / 360°) × pi ×r^2

= (2/ 360°) × pi × (5)^2

=.( 1/180°) × pi × 25

replace 180° with pi

1/pi × pi ×25

Area of sector is 25cm^2


Thanks