In figure ABC is a triangle right angled at B with AB=14cm and BC=24cm with vertices A,B and C as center arces are drawn, each of radius 7cm. Find area of shaded region.

Radius of each sector (r) = 7 cm
Let θ1 ,θ2and θ3 be the angles of sectors (angle of triangle)
⇒ θ1+θ2+θ3=180∘(Angle sum-property)

Area of shaded region = Area of ΔAC – Area of 3 sectors
                                      =12×AB×BC−πr2360∘[θ1+θ2+θ3][Area of sector=πr2θ360∘]
                                      =12×14×24−π×7×7360∘​×180∘  [AB = 14 cm, BC = 24 cm(given)]
                                      =168−227×7×72
                                      =168−11×7
                                       = 168 – 77
                                       =91 cm²