Q. 104.0( 204 Votes )

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 :

By Jyoti’s diagram,


Area of pentagon = Area of trapezium ABCP + Area of trapezium AEDP

we know area of trapezium = 1/2 × (Sum of parallel lines) × (Distance between parallel lines)

= 1/2 (AP + BC) × CP + 1/2 (ED + AP) × DP = 1/2 (30 + 15 ) × CP + 1/2 (15 + 30) × DP


= 1/2 (30 + 15) (CP + DP)


= 1/2 × 45 × CD


= 1/2 × 45 × 15


=337.5 m2

By Kavita's diagram,

Area of pentagon = Area of square ABCD + Area of triangle ABP
we know, 
area of square = (side)2  = side × side
area of triangle = (1/2) × base x Height

AB×AB  +  1/2(AB×h)

= 15×15 + ½(15×15)

= 225 + 225/2

=225+112.5 = 337.5 m2

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