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Online Quiz (Worksheet A B C D)

Questions Per Quiz = 2 4 6 8 10

Grade 7 - Mathematics
9.45 Area of Rectangular Path - II

Example:
A path of 2 metres wide runs around and inside a rectangular plot of measurements 30 metres and 20 metres. Find the cost levelling the path at the rate of $2 per square metre.

Solution:
Given that,
the length = 30 metres, width = 20 metres, width of the path = 2 metres
Since the path runs inside this, the measurements of the inner rectangle are,
(l - 2w) and (b - 2w)
i.e (30 - 2*2) and (20 - 2*2)
i.e (30 - 4) and (20 - 4)
i.e 26 and 16
The area of the given rectangle = l * b = 30 * 20 = 60 square metres.
The area of the inner rectangle = (l - 2w)(b - 2w) = 26 * 16 = 416 square metres.
So the area of the path = lb - (l - 2w)(b - 2w)
= 600 - 416
= 184 square metres.
The cost of levelling the path at the rate of $2 per square metres.
= $ 2 * 184 = $ 368.


Directions: Read the above example carefully and answer the following questions:

  • Draw a rectangular plot of side 11 centi-metres and 13 centimetres. Draw a path of width 3 centi-metres, around and outside the rectangular plot. Find the cost of leveling the path at the rate of $3 per square metre. Use different colors to represent the path and the rectangular plot.



Q 1: A path runs around and inside a rectangular plot of measurements 18 metres and 13 metres. Find the width of the path if the area of the path is given by 130 square metres.
2.5 metres
2.3 metres
1.6 metres
1.4 metres

Q 2: A path of 3 metres wide runs around and inside a rectangular plot of measurements 26 metres and 22 metres. Find the cost of leveling the path at the rate of $2 per square metre.
$ 352
$152
$95
$ 504

Q 3: A path of 2 metres wide runs around and inside a rectangular plot of measurements 15 metres and 12 metres. Find the cost of leveling the path at the rate of $3 per square metre.
$216
$ 300
$ 276
$ 246

Q 4: A path of 1 metre wide runs around and inside a rectangular plot of measurements 20 metres and 15 metres. Find the area of the path.
76 square metres
96 square metres
86 square metres
66 square metres

Question 5: This question is available to subscribers only!

Question 6: This question is available to subscribers only!


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