A circular segment is enclosed between a secant/chord and the arc whose endpoints equal the chord's.

In our case we need to find the area of the circular segment with secant/chord of length 15 cm and radii 10 cm.

The area of the circular segment is equal to the area of the circular sector minus the area of the triangular portion.

Area of Segment = ½ × (θ - sin θ) × r^2 (when θ is in radians)

we have r = 10 cm, we need to find θ.

θ = the angle above the chords with length 15 cm. Using the definition for sinus we find

sin(θ/2) = (c/2) / r = c/2*r = 15 / 20 = 7.5 /10

θ = 2 arcsin (7.5 /10)

θ = 2*0.848 = 1.696 rad

sin θ = 0.992

Area of Segment = ½ × (θ - sin θ) × r^2 = ½ × (1.696 - 0.992) × 10^2

Area of Segment = 35.2 cm^2.