Question

There is a pentagonal shaped park as shown in Fig. 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 area?

Answer 1

Area of given figure = Area of trapezium + area of rectangle

Area of Jyoti’s diagram = 2 x \(\frac{1}{2}\) x (sum of parallel sides) x altitude

Area of given figure = 2 x \(\frac{1}{2}\) x (15 + 30) x 7.5

Area of given figure = 337.5 cm²

Therefore area of given figure is 54 cm²

Area of given pentagon = Area of triangle + area of rectangle

Area of given pentagon = \(\frac{1}{2}\) x base x altitude + length x breadth

Area of given pentagon = \(\frac{1}{2}\) x 15 x 15 + 15 x 15

Area of given pentagon = 112.5 + 225 = 337.5

Therefore area of given pentagon is 337.5 cm²