Question

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

Answer 1

We can divide the field into three triangles and one trapezium.
Let A, B, C be the three triangular regions and D be the trapezoidal region.
Now,
Area of A = `1/2` x AD x GE

                = `1/2` x ( 50 + 40 + 15 + 25 ) x 60

                = 3900 sq.m 

Area of B = `1/2` x AF x BF

                = `1/2` x 50 x 50

                = 1250 sq.m

Area of C = `1/2` x HD x CH

                = `1/2` x 25 x 25

                = 312.5 sq.m.

Area of D = `1/2` x ( BF + CH ) x ( FG + GH )

                = `1/2` x ( 50 + 25 ) x ( 40 + 15 )

               = `1/2` x 75 x 55 
               = 2062.5 sq.cm     

Area of the figure = Area of A + Area of B + Area of C + Area of D
= 3900 + 1250 + 312.5 + 2062.5
= 7525 sq.m