There is a pentagonal shaped park as shown in the figure. For finding its area Jyoti and Kavita divided it in two different ways. Find the area of this park using both ways. Can you suggest some other way of finding its area?

(i) By Jyoti's diagram:

Area of pentagon = Area of trapezium ABCD + Area of trapezium AFED

= 2 × Area of trapezium ABCD (Since,  Area of trapezium ABCD = Area of trapezium AFED )

=$2 \times \frac{1}{2} (a + b) \times h$
$= (15 + 30) \times 7.5 = 45 \times 7.5 = 337.5 m^2$

(ii)  By Kavita's diagram:

Area of the pentagonal shape = Area of ∆ABE + Area of square BCDE
$= \frac{1}{2}\times b\times h + 15\times 15 = 12\times 15\times 15 + 225 = 112.5+225 = 337.5 m^2$

Another way:

HereArea of ΔAFB = Area of ΔCGB

Also, B is the midpoint of FG. Thus, FB = BG = 7.5 m

GC = AF = 30 - 15 = 15 m

Area ABCDE = Area of rectangle GFED – (Area of ΔAFB + Area of ΔCGB)

= GD × ED - 2 × [1/2 × FB × AF]

= 30 × 15  − 2 × [1/2 × 7.5 × 15]

= 450 - 112.5  = 337.5 m²