Find the area of the following polygon if AB = 12 cm, AC = 2.4 cm, CE = 6 cm, AD = 4.8 cm, CF = GE = 3.6 cm, DH = 2.4 cm.

BE = AB – AE

= 12 cm – (AC + CE)

= 12 cm – (2.4 cm + 6 cm)

= 12 cm – 8.4 cm = 3.6 cm

=1/2×3.6×3.6=6.48 cm²

Area of ∆ABH = 1/2 × b × h = 1/2 × AB × DH

= 1/2 × 12 × 2.4 cm = 14.4 cm²

Area of ∆ACF = 1/2 × b × h =  1/2 × CF × AC

= 1/2 × 3.6 × 2.4 = 4.32 cm²

Area of the rectangle FCEG = l × b

= CE × CF

= 6 cm × 3.6  = 21.6 cm²

Area of ∆GEB = 1/2 × b × h = 1/2 × BE × GE

= 1/2 × 3.6 × 3.6 = 6.48 cm²

Area of ∆ABH = 1/2 × b × h = 1/2 × AB × DH

= 1/2 × 12 × 2.4 = 14.4 cm²

Area of the polygon AFGBH = Area of ∆ACF + Area of rectangle FCEG + Area of ∆GEB + Area of ∆ABH

= 3.6 cm² + 4.32 cm² + 21.6 cm² + 6.48 cm² + 14.4 cm²

= 50.40 cm²

Hence, the required area = 50.40 cm².