(a) Find the area of the polygonal regions given.
C
B
30m
20 m
H
15ml 15 m
D
20 m
А
G
10 m 20m
40m
30ml
E
F
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Answer:
Area of all triangles = Area of triangle AFM + Area of triangle EOD + Area of triangle ALB + Area of triangle NCD =
2
1
×AM×FM+
2
1
×EO×OD+
2
1
×AL×LB+
2
1
×ND×NC
2
1
×20×20+
2
1
×60×30+
2
1
×10×30+
2
1
×40×40
200+900+150+800=2050
Area of all trapezium = Area of FMOE+ Area of LNCB
2
1
(FM+EO)×MO+1/2×(LB+NC)×LN
2
1
×(20+60)×40+1/2×(30+40)×40
=3000
area of the polygon =Area of all triangles + Area of all trapezium
A=2050+3000=5050cm
2
Answer (D) 5050cm
2
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