Curvature system: S=lr/2=a*r*r/2.

Let the straight line distance at both ends of the arc be = a, and the distance from the midpoint of the straight line to the midpoint of the arc be = b (A and B are known and constant).

Let radius = r, then

(r-b)^2 +(a/2)^2=r^2

Solution, r = [(a 2)/4+b 2]/2b = (a 2)/(8b)+b/2.

Find r, you can find the angle corresponding to the arc, and then find the area of the arc.

Extended data:

The calculation formula of arc length is a mathematical formula, L=n (degree of central angle) × π( 1)× r (radius)/180 (angle system), L=α (radian )× r (radius system). Where n is the degree of central angle, r is the radius, and l is the arc length of central angle.

L = n (central angle) ×π(π)× r (radius)/180=α (radian of central angle )× r (radius)

In a circle with radius r, because the arc length subtended by the central angle 360 is equal to the circumference of the circle C=2πr, the arc length subtended by the central angle n is L = n π r ÷ 180 (L = n X2π r/360).

Example: The radius is 1cm, and the arc length corresponding to the central angle of 45 is

l=nπr/ 180

=45×π× 1/ 180

=45×3. 14× 1/ 180

Approximately equal to 0.785

The second formula for the arc length of the sector is:

The arc length of the sector is actually a side length of the circle, and the angle of the sector is a fraction of 360 degrees, so the arc length of the sector is a fraction of the circumference of the circle, so the following conclusions can be drawn:

Sector arc length =2πr× angle /360

Where 2πr is the circle and the angle is the angle value of the sector.