Question

There is a pentagon shaped park as shown in the figure. For finding its area Jyoti and Kavita divided it in two different ways,

Find the area of the above figure using either Jyothi's diagram or kavitha's diagram.

• A. Area = $837.5m^2$
• B. Area = $307.5m^2$
• C. Area = $537.5m^2$
• D. Area = $337.5m^2$

Answer 1

The correct option is D

Area = $337.5m^2$

First way : By Jyoti's diagram,
Area of pentagon = Area of trapezium ABCP + Area of trapezium AECP

$=\frac{1}{2}(AP+BC)\times CP+\frac{1}{2}(ED+AP)\times DP=\frac{1}{2}(30+15)\times CP+\frac{1}{2}(15+30)\times DP=\frac{1}{2}(30+15)(CP+DP)=\frac{1}{2}\times 45\times CD=\frac{1}{2}\times 45\times 15=337.5m^5$
Second way : By Kavita's diagram
Here, a perpendicular AM has to be drawn to BE
AM = 30 - 15 = 15 m
Area of pentagon = Area of $\Delta$ ABE + Area of square BCDE

$=\frac{1}{2}\times 15\times 15+15\times 15=112.5+225.0=337.5m^2$
Hence total area of the pentagon shaped park = $337.5m^2$