Question

In the given figure, find the area of the field shown alongside. All
dimensions are in metres.

C
R
20
Q
40
E
30
Р
20
B
30120​

Answer 1

Step-by-step explanation:

The area of pentagonal field

ABCDE=A(△ABC)+A(△AFE)+A[trapeziumEFDH+A(△DHC)]

Area of △ABC=

2

1

×base×height

=

2

1

×AC×BG[AC=AF+FG+GH+HC=50+50+40+30=170]

=

2

1

×170×50

=85×50

=4250m

2

Area of △AFE=

2

1

×base×height

=

2

1

×FA×EF

=

2

1

×50×30

=50×15

=750m

2

Area of trapezium EFDH=

2

1

×(sum of parallel sides)×height

=

2

1

×(EF+DH)×HF[HF+HG+GF=50+40=90]

=

2

1

×(30+20)×90

=

2

1

×50×90

=50×45

=2250m

2

Area of △DHC=

2

1

×base×height

=

2

1

×DH×CH

=

2

1

×20×30

=10×30

=300m

2

Therefore,

Area of pentagonal field =A(△ABC)+A(△AFE)+A[trapeziumEFDH+A(△DHC)]

=4250+750+2250+300

=7550m

2

The area of pentagonal field is 7550m

2