Find the area of the following polygon. Given AD = 10 cm, AH = 8 cm, AG = 4 cm, AF = CH = 3 cm, BF = EG = 2.5 cm. В. С А D F G H E
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Polygon ABCDE is divided into parts as shown in the given figure. Find its area if AD=8cm,AH=6cm,AG=4cm,AF=3cm and perpendiculars BF=2cm,CH=3cm,EG=2.5cm
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In the given figure,
ABCDE, AD=8cm,AH=6cm,AG=4cm,AF=3cm
BF=2cm,CH=3cm and EG=2.5cm
The given figure consists of 3 triangles and one trapezium.
Now
Area of △AED=
2
1
×AD×GE=
2
1
×8×2.5=10cm
2
Area of △ABF=
2
1
×AF×BF=
2
1
×3×2=3cm
2
Area of △CDH=
2
1
×HD×CH=
2
1
×(AD−AH)×3
=
2
1
×(8−6)×3=
2
1
×2×3=3cm
2
Area of trapezium BFHC=
2
1
×(BF+CH)×FH
=
2
1
×(2+3)×(AH−AF)
=
2
1
×5×(6−3)=
2
1
×5×3=7.5cm
2
Hence,
Total area of the figure = Area of △AED + Area of △ABF + Area of △CDH + Area of trapezium BFHC
=10+3+3+7.5=23.5cm
2