Question

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?

Answer 1

(i) Jyoti’s way of finding the area is as follows:

Area of pentagon ABCDE = Area of trapezium ABCF + Area of trapezium AEDF
\(= \frac{1}{2} × (AF + BC) × FC + \frac{1}{2} × (AF + ED) × DF\)

\(= \frac{1}{2} × (30 m + 15 m) × \frac{15}{2} m + \frac{1}{2} × (30 + 15 m) × \frac{15}{2} m\)

\(= 2 × \frac{1}{2} (30 m + 15 m) × \frac{15}{2}\)
\(= 45 m × 7.5 m\)
\(= 337.5 m²\)

Thus, the area of the pentagonal shaped park according to Jyoti’s way is 337.5 m²

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(ii) Kavitha’s way of finding the area is as follows:

Area of pentagon ABCDE = Area of triangle ABE + Area of square EBCD
\(= \frac{1}{2} × BE × (AF − OF) + FC × BC \)     [Since, AO = AF - OF]

\(= \frac{1}{2} × 15 × (30 − 15) + (15 × 15 )\)

\(= (\frac{1}{2} × 15 × 15) m² + 225 m²\)
\(= 112.5 m² + 225 m²\)
\(= 337.5 m²\)

Thus, the area of the pentagonal shaped park according to Kavitha’s way is 337.5 m²