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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?
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Solution
Jyoti's way,
Area of field ABDEC = 2 area of (ABDF)
`2 xx 1/2 [(BD + AF) xxDF]`
= `[(15 + 30) xx 15/2] m^2`
= `((45 xx 15)/2) m^2`
= 337.5m2
Kavita way's
Area of field ABCDE
Area of ΔABE + Area of BEDC
= `1/2 xx (BE xx AF) + (BF xx ED)`
= `1/2 xx(15 xx 15) + (15 xx 15)`
= `{1/2 (225) + 225} m^2`
= 337.5 m2
Yes, we have also some other way of finding its area.
Area of field ABEDC
= Area of ΔABC + ΔCDE + ΔBCE
= `1/2 xx AF xx BC + 1/2 xx CD xx ED + 1/2 xxBC xx BE`
= `3 (1/2 xx 15 xx 15) m^2`
= 337.5 m2
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