Question

Polygon ABCDE is divided in different parts as shown in figure. If AD = 8 cm, AH = 6 cm, AG = 4 cm, AF = 3 cm and BF = 2 cm, CH = 3cm, EG = 2.5 cm. Then find the area of the polygon.

Answer 1

Area of polygon ABCDE = Area of right ΔAFB + Area of trapezium BFHC + Area of right ΔCHD + Area of right ΔEGD + Area of right ΔAGE

`= 1/2 xx "AF" xx "BF" + 1/2 xx ["BF + CH"] xx "FH" + 1/2 xx "HD" xx "CH" + 1/2 xx "GD" xx "GE" + 1/2 xx "AG" xx "GE"`

`= 1/2 xx 3 xx 2 + 1/2 xx [2 + 3] xx [6 – 3] + 1/2 xx [8 – 6] xx 3 + 1/2 xx [8 – 4] xx 2.5 + 1/2 xx 4 xx 2.5`

= 3 + 7.5 + 3 + 5 + 5

= 23.5 cm²