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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 of 1.5 metres wide runs around and inside a rectangular plot of measurements 15 metres and 10 metres. Find the area of the path.
76 square metres
66 square metres
86 square metres
96 square metres

Q 2: 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.
$ 300
$216
$ 276
$ 246

Q 3: 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.
$ 504
$95
$ 352
$152

Q 4: A path runs around and inside a rectangular plot of measurements 16 metres and 14 metres. Find the width of the path if the area of the path is given by 104 square metres.
9 metres
3 metres
2 metres
8 metres

Question 5: This question is available to subscribers only!

Question 6: This question is available to subscribers only!


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