Question

There is a pentagonal park. Neha and Midhi divided it in two different ways to
find its area.
28 m
15 m
15 m
12 m
Nidhi's figure
Neha's figure
Fig. 14.13
Find the area of the park in both ways.​

Answer 1

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,

Answer 2

Answer:

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