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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 -

(i)From Jyoti’s diagram:

Area of the pentagonal shape = Area of trapezium ABCD + Area of trapezium ADEF
= 2 × Area of trapezium ABCD
= 2 × 
1 (a+ b) × h
= (15 + 30) × 7.5
= 45 × 7.5
= 337.5 m2
(ii) From Kavita’s diagram:

Area of the pentagonal shape = Area of ∆ABE + Area of square BCDE
1 ×b × h + 15 × 15
1 ×15 × 15 + 225
= 112.5 + 225
= 337.5 m2

Yes, we can also find the other way to calculate the area of the givenpentagonal shape.
Join CE to divide the figure into two parts, i.e., trapezium ABCE and righttriangle EDC.
Area of ABCDE = Area of ∆EDC + Area of square ABCE

 

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