Question

E
24. The following
diagram shows
pentagonal
field ABCDE
in which the
lengths of AF
FG, GH and HD
are 50 m. 40 m
CH
15 m and 25 m
respectively, and
the lengths of
perpendiculars BF, CH und EG are 50 m, 25
m and 60 m respectively. Determine the area
of the field​

Answer 1

Step-by-step explanation:

we can divide the field into 3 triangles and 1 trapezium .

let A, B, C be the 3 triangular regions and D be the trapezodial region .

Now

Area of A= 1/2×AD×GE

=1/2× (50+40+15+25)×60

=3900 sq.m

Area of B= 1/2×AF×BF

=1/2×50×50

=1250 sq.m

Area of C=1/2×HD×CH

=1/2× 25×25

= 312.5 sq.m

Area of D=1/2 ×(BF+CH) ×(FG+GH)

=1/2×(50+25)×(40+15)

=1/2×75×55

=2062.5 sq. m

Total Area of Figure=Area of A + Area of B + Area of C + Area of D

=3900+1350+312.5+2062.5

=7525 sq. m