The following figure shows a pentagonal-shaped park.

If Jyoti and Kavita were asked to find the area of the park, then what could be the area of the park?

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337.5 m2

437.5 m2

338 m2

337 m2

answer is A.

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Detailed Solution

The figure is,
Question Image

First, we will solve Jyoti's approach for solving the area of the pentagon.
The figure is divided into two trapeziums.
Question Image

Given, AP = 30 m and BC = CD = DE = 15 m.
From figure,
CP + PD = CD = 15m ------- (1)
Also, we will use formula,
Area of pentagon
= Area of trapezium ABCP + Area of trapezium AEDP

⇒ 12 B C + A P C P + 12 E D + A P P D ⇒ 12 15 + 30 C P + 12 15 + 30 P D

⇒ 1245 C P + 1245 P D ⇒ 12 × 45 C P + P D

Using equation (1), we will get,

⇒ 22.5 × C D ⇒ 22.5 × 15 ⇒ 337.5 m 2

Next, we will solve Kavita's approach for solving the area of the pentagon.
The figure is divided into a triangle ABE and a rectangle BCDE.
Question Image

Given, BE = BC = CD = DE = 15m and AP = 15m.
Also, we will use the formula,
Area of pentagon
= Area of triangle ABE + Area of rectangle BCDE

⇒ 12 × A P × B E + C D × B C

Substituting the values, we will get,

⇒ 12 × 15 × 15 + 15 × 15

⇒ 112.5 + 225 ⇒ 337.5 m 2

Thus, there may be many possibilities of dividing this given pentagon to find its area, but Joyti’s and Kavita’s diagrams are the two most-simple ways of solving it.
Hence, the area of the pentagon is 337.5 m2.
Thus, option (1) is correct.

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