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