In Fig. 10, ABC is a triangle right-angled at B, with AB = 14 cm and BC = 24 cm. With the vertices A, B and C as centers, arcs are drawn, each of radius 7 cm. Find the area of the shaded region. [Use π = 22/7]

Base of the tringle = BC = 24 cm

Height of the triangle = BA = 14 cm

Therefore, Area of the triangle ABC = 1/2 × Base × Height

= 1/2 × 24 × 14

= 168 cm²

Radius of each sector = r = 7 cm.

AB = 18 cm, DC = 32 cm

Distance between AB and DC = Height = 14 cm

Now, Area of the trapezium = (1/2) × (Sum of parallel sides) × Height

= (1/2) × (18 + 32) × 14 = 350cm²

As AB ∥ DC, ∴ ∠ A + ∠ D = 180°

and ∠ B + ∠ C = 180°

Also, radius of each arc = 7 cm

Therefore,

Area of the sector with central angle A = (1/2) × (∠A/180) × π × r²

Area of the sector with central angle B (1/2) × (∠B/180) × π × r²

Area of the sector with central angle C = (1/2) × (∠C/180) × π × r²

Total area of the sectors =

(∵ Sum of all angles of a triangle is 180°)

= 77 cm²

∴ Area of shaded region = Area of triangle – (Total area of sectors)

= 168 – 77 = 91 cm²

Hence, the required area of shaded region is 91 cm².