 # There is a pentagonal shaped park as shown in Fig. 20.50. Jyoti and Kavita divided it in two different ways.

Question:

There is a pentagonal shaped park as shown in Fig. 20.50. Jyoti and Kavita divided it in two different ways. Find the area of this park using both ways. Can you suggest some another way of finding its areas?

Solution:

A pentagonal park is given below: Jyoti and Kavita divided it in two different ways.

(i) Jyoti divided is into two trapeziums as shown below:

It is clear that the park is divided in two equal trapeziums whose parallel sides are $30 \mathrm{~m}$ and $15 \mathrm{~m}$.

And, the distance between the two parallel lines: $\frac{15}{2}=7.5 \mathrm{~m}$

$\therefore$ Area of the park $=2 \times($ Area of a trapazium $)$

$=2 \times\left[\frac{1}{2} \times(30+15) \times(7.5)\right]$

$=337.5 \mathrm{~m}^{2}$

(ii) Kavita divided the park into a rectangle and a triangle, as shown in the figure.

Here, the height of the triangle $=30-15=15 \mathrm{~m}$

$\therefore$ Area of the park $=$ (Area of square with sides $15 \mathrm{~cm}$ ) $+$ (Area of triangle with base $15 \mathrm{~m}$ and altitude $15 \mathrm{~m}$ )

$=(15 \times 15)+\left(\frac{1}{2} \times 15 \times 15\right)$

$=225+112.5$

$=337.5 \mathrm{~m}^{2}$