Let 'R' represent the radius of the circle.

The perimeter of a quarter circle is equal to (1/4)2*R*pi = R*pi/2.

Since the perimeter of a quarter circle is 10.71 meters we have:

R*pi/2 = 10.71

R = 10.71*2/pi

The area of the circle is:

A = R^2*pi

Plug the value for R = 10.71*2/pi into A = R^2*pi:

A = (10.71*2/pi)^2*pi

A = 10.71*2/pi

Quarter area is:

(1/4)A = 10.71*2/(pi*4)

(1/4)A = 10.71/(pi*2)

(1/4)A = 10.71/(3.14*2) (since pi = 3.14)

(1/4)A =  1.71 m^2

The quarter circle's area is 1.71 m^2.