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
Answers
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:
Yes
Step-by-step explanation:
It's ok