Question

There is a pentagonal park. Neha and Nidhi divided it in two different ways to find its area.
Find the area of the park in both ways.​

Answer 1

Answer:

1. 258

Step-by-step explanation:

in Neha's figure

it forms the shape of trapezium

Area of trapezium = 1/2(sum of parallel sides)×height

1/2(28+15)×12

(43)×6

258

in Nidhi's figure

it forms triangle and rectangle

Area of triangle = 1/2× base×height

1/2×12×13

6×13

78

Now

Area of rectangle = length×height

12×15 = 180

now,area of figure = area of triangle + area of rectangle = 78+180=258

Answer 2

Answer:

Consider the given pentagonal park.

Let us find the area of the park which Neha divided.

Neha divided the pentagonal park into two trapezoids.

So, area of the park = 2 \times2× Area of trapezoid

= 2 \times \frac{(a+b) h}{2}2×

2

(a+b)h

where 'a' and 'b' are the lengths of the parallel sides of the trapezoid and 'h' is the height

= 2 \times \frac{(15+28) \times 6}{2}2×

2

(15+28)×6

= 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

= \frac{1}{2} bh + lw

2

1

bh+lw

where 'b' is base and 'h' is height of the triangle and 'l' is length and 'w' is width of the rectangle.

=(\frac{1}{2} \times 12 \times 13) + (15 \times 12)(

2

1

×12×13)+(15×12)

= 78 + 18078+180

= 258 square meters.

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