Question

B
G
15. Polygon ABCDE is divided into parts as shown in
adjoining figure. Find its area if AD = 8 cm, AH =
6 cm, AG = 4 cm, AF = 3 cm and perpendiculars
BF = 2 cm, CH = 3 cm, EG = 2.5 cm.
A
F
-D
E​

Answer 1

Answer:

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Step to step Explanation:

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=

1/2×AD×GE= 1/2×8×2.5=10cm

Area of △ABF= 1/2 ×AF×BF= 1/2 ×3×2=3cm

Area of △CDH= 1/2×HD×CH

1/2 ×(AD−AH)×3

1/2×(8−6)×3

1/2×2×3=3cm

Area of trapezium BFHC=

1/2 ×(BF+CH)×FH= 1/2×(2+3)×(AH−AF)

1/2×5×(6−3)

1/2×5×3=7.5cm

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