Question

Find the area of the above pentagon ABCDE in which BG is perpendicular on AC, EF is perpendicular on AD and DH is perpendicular on AC. AD = 10 cm, AC = 12 cm, EF = 3 cm, DH = 7 cm, BG = 5 cm.

Answer 1

Answer:

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