Question

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


​

Answer 1

First way: By Jyoti’s diagram,

Formula:

Area of pentagon = Area of trapezium ABCP + Area of trapezium AEDP

= (½)(AP+BC)×CP+(1/2)×(ED+AP)×DP

= (½)(30+15)×CP+(1/2)×(15+30)×DP

= (½)×(30+15)×(CP+DP)

= (½)×45×CD

= (1/2)×45×15

=337.5 m²

Area of pentagon is 337.5 m²

Second way: By Kavita’s diagram,

Here, a perpendicular AM drawn to BE.

AM = 30–15 = 15 m

Area of pentagon = Area of triangle ABE+Area of square BCDE (from above figure)

= (½)×15×15+(15×15)

= 112.5+225.0

= 337.5 m²

Hence, total area of pentagon shaped park = 337.5 m²