Question

if the perimeter of a sector is P units and its radius is R units then its area​

Answer 1

Given: Perimeter of a sector is P units,  radius is R units.

To find: Area?

Solution:

• As we have given that perimeter is P units of a sector, so P will be:

             P = 2R + X

             X = P - 2R

            Here arc length of the sector is X.

• Now we know the formula for arc length, that is:

            X = Ф/360 x 2πR   

            where Ф is the angle of the sector.

            Ф = 360X/2πR

            Ф = 180X/πR

• Now area of the sector is: 1/2 r²Ф

             putting these values in the formula, we get:

             = 1/2 (R)² 180X/πR

             = 90R/π unit².

Answer:

           So the area of the sector will be   90R/π unit².