Question

Find the area of the shaded region of the adjoining figure, it being given that
FAB = angle CBA = 90°, ED || AB || FC, EG I FC, DH I FC, FG = HC, AB =
15 cm, AF = 9 cm, ED = 8 cm and distance between AB and ED = 13 cm.
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Answer 1

In the figure, FAB = angle CBA = 90°, ED || AB || FC, EG I FC, DH I FC, FG = HC, AB =  15 cm, AF = 9 cm, ED = 8 cm and distance between AB and ED = 13 cm.

Consider the attached figure while going through the following steps.

Area of polygon ABCDEFA is

= Area of rectangle ABCF

+ Area of trapezium CDEF

Area of rectangle ABCF = AB × AF

= 15 × 9

= 135 cm²

Area of trapezium CDEF = (FC + ED)/2 + EG

EG = BD - BC = BD - AF = 13 - 9

EG = 4 cm

Area = (15 + 8)/2 + 4

= 23/2 + 4

= 15.5 cm²

Area of polygon ABCDEFA  = 135 + 15.5 = 150.5 cm²