Question

You
must
have
observed
that
quite
often,


in
gardens
or
parks,
some
space
is
left
all


around
in
the
form
of
path
or
in
between


as
cross
paths.
A
framed
picture
has
some


space
left
all
around
it.We
need
to
find


the
areas
of
such
pathways
or
borders


when


we
want
to
find
the
cost
of
making
them.


A
rectangular
park
is
45
m
long
and
30
m


wide.A
path
2.5
m
wide
is
constructedoutside
the
park.
Find
the
area
of
the path​

Answer 1

Answer:

a unit of area to a larger unit, the number of larger units will be

smaller.

1000

For example, 1000 cm = m = 0.1 m 2

2

2

10000

TRY THESE

Convert the following:

2

2

2

(i) 50 cm in mm 2 (ii) 2 ha in m 2 (iii) 10 m in cm 2 (iv) 1000 cm in m 2

11.7 APPLICATIONS

You must have observed that quite often, in gardens or parks, some space is left all around

in the form of path or in between as cross paths. A framed picture has some space left all

around it.

We need to find the areas of such pathways or borders when

P Q

we want to find the cost of making them. 2.5 m

A 45 m B

EXAMPLE 20 A rectangular park is 45 m long and 30 m wide.

A path 2.5 m wide is constructed outside the

park. Find the area of the path. 30 m 2.5 m

SOLUTION Let ABCD represent the rectangular park and

D C

the shaded region represent the path 2.5 m wide.

S R

To find the area of the path, we need to find (Area of rectangle

PQRS – Area of rectangle ABCD).

We have, PQ = (45 + 2.5 + 2.5) m = 50 m

PS = (30 + 2.5 + 2.5) m = 35 m

2

Area of the rectangle ABCD = l× b = 45 × 30 m = 1350 m 2

2

Area of the rectangle PQRS = l× b = 50 × 35 m = 1750 m 2

Area of the path = Area of the rectangle PQRS − Area of the rectangle ABCD

= (1750 − 1350) m = 400 m 2

2

EXAMPLE 21 A path 5 m wide runs along inside a square park of side

A 100 B

100 m. Find the area of the path. Also find the cost of

2

cementing it at the rate of  250 per 10 m .

P Q

SOLUTION Let ABCD be the square park of side 100 m. The

shaded region represents the path 5 m wide.

PQ = 100 – (5 + 5) = 90 m

2

2

2

Area of square ABCD = (side) = (100) m = 10000 m 2

S R

Area of square PQRS = (side) = (90) m = 8100 m 2

2

2

2

2

Therefore, area of the path = (10000 − 8100) m = 1900 m 2

D C

Cost of cementing 10 m =  250

2

Answer 2

Answer:

Yes

Step-by-step explanation:

It's ok