Question

There is a pentagonally 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.

• A. $337.5m^2$
• B. $337.5c{m}^2$
• C. $33.5m^2$
• D. None of these

Answer 1

The correct option is A $337.5m^2$

Taking Jyoti's diagram
Area of the pentagonal shaped park
$2\times AreaoftrapeziumABEF$
$=2\times \frac{1}{2}\times (15+30)\times \frac{15}{2}{m}^2$
$=\left(\begin{array}{c}45\times \frac{5}{2}\end{array}\right)m^2=337.5m^2$.
Taking Kavita's diagram
Area of the pentagonal shaped park
$=Area\left(squareABCE\right)+Area\left(\Delta DEF\right)$
$=15\times 15+\frac{1}{2}\times 15\times 15$
$=225+\frac{225}{2}=225+112.5=337.5m^2$