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?

First way: By Jyoti’s diagram,
Area of pentagon = Area of trapezium ABCP + Area of trapezium AEDP
= 1/2(AP+BC) x CP+1/2 (ED + AP) x DP
= 1/2(30+15) x CP+1/2 (15 + 30) x DP
= 1/2(30+15) x (CP+DP)
= 1/2x45xcd= 1/2x45x15=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 ∆ABE + Area of square BCDE
=1/2x15x15+15×15=112.5+225.0=337.5 m²
Hence, total area of pentagon shaped park = 337.5 m².

Class 8 Maths Chapter 11 Exercise 11.2 Solution in Video

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https://www.tiwariacademy.com/ncert-solutions/class-8/maths/chapter-11/