Question

There is a pentagonal park. Neha and Nidhi divided it into two different ways to find its area.
Find the area of the park in both ways. (Picture is attached)

Answer 1

Given : Pentagonal park.

To find : Area of the park.

Neha divided the pentagonal park into two trapezoids.

So, area of the park = 2 \times Area of trapezoid

= 2 * (a + b)h / 2 ... ( 1)

where

'a' and 'b' are the lengths of the parallel sides of the trapezoid and

'h' is the height

Equating in (1)

= 2 * (15 + 28 ) * 6 / 2

= 258 square meters.

Now, let us find the area of the park which Nidhi divided.

Nidhi divided the park into one triangle and one rectangle.

So, area of the park = area of triangle + area of rectangle

= 1/2bh + lw

where 'b' is base

'h' is height of the triangle

'l' is length and

'w' is width of the rectangle.

= (1/2 * 12 * 13 ) + ( 15 * 12 )

= 78 + 180

= 258 square meters.

So, the area of the given pentagonal park is 258 square meters,

Answer 2

Answer:

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