the perimeter of a sector of acircle of radius 4 2cm is 12 8cm, find the area of the sector - Maths - Areas Related to Circles

Question

the perimeter of a sector of acircle of radius 4 2cm is 12 8cm,
find the area of the sector

Ajanta Trivedi · Accepted Answer

let the radius of the circle be r = 4 2 cm let the arc length AB be p cm the perimeter of the sector AOB = p+2r therefore, p+2r=12 8 p+2*4 2=12 8 p+8 4=12 8 p=12 8-8 4 p = 4 4 cm the length of the arc = 4 4 cm the circumference of the circle = $2 π r = 2 * \frac{22}{7} * 4 2 = 26 4 c m$ let the sector makes an angle Î¸ with the center therefore $θ = \frac{2 π r}{360} * 4 4 = \frac{26 4}{360} * 4 4 = \frac{1 1}{15} * 4 4 = \frac{4 84}{15}$ $θ = \frac{484}{1500} = 0 3227$ area of the sector = $π r^{2} * \frac{θ}{360} = \frac{22}{7} * 4 2 * 4 2 * \frac{0 3227}{360} = 0 0497 c m^{2}$ hope this helps you

the perimeter of a sector of acircle of radius 4.2cm is 12.8cm, find the area of the sector.