Question

There is a Pentagonal shaped parts as shown in the figure. for finding its area jyoti and Kavita divided it in two different ways
​

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