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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

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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.

Sum
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Solution

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     

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Chapter 20: Area and Perimeter of Plane Figures - Exercise 20 (B) [Page 256]

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Selina Concise Mathematics [English] Class 9 ICSE
Chapter 20 Area and Perimeter of Plane Figures
Exercise 20 (B) | Q 24 | Page 256

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