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Online Quiz (Worksheet A B C D)

Questions Per Quiz = 2 4 6 8 10

Grade 7 - Mathematics
9.47 Area of Rectangular Path - IV

Example:
The length and width of a rectangular plot are 30 metres and 20 metres respectively. Two rectangular paths each 5 metres wide run inside the plot, one parallel to the length of the plot and the other parallel to its width. Find the total area occupied by the paths.

Solution:
To solve this type of problems first we draw a rough diagram and mention the given measurements.

In the above diagram, ABCD is the given plot (length 30 metres and breadth 20 metres) and KLMN and PQRS are the two rectangular paths running parallel to its length and width respectively, the width of each of these paths is 5 metres.
The area of the path KLMN = 30 * 5 = 150 square metres.
The area of the path PQRS = 20 * 5 = 100 square metres.
The area of the path EFGH,
which is common to these two paths = 5 * 5 = 25 square metres.
Now,
The total area occupied by the paths = (The area of the rectangle KLMN) + (The area of the rectangle PQRS) - (The area of the square EFGH)
So the required are = 150 + 100 - 25
= 225 square metres.

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

  • Draw a rectangular plot of length 11 centi-metres and width 9 centi-metres. Draw two rectangular paths each 4 centi-metres wide run inside the plot, one parallel to the length of the plot and the other parallel to its width. Find the total area occupied by the paths.



Q 1: The length of a rectangular plot is 25 metres. Two rectangular paths each 2 m wide run inside the plot, one parallel to the length of the plot and the other parallel to its width. Find the width of the plot if the total area occupied by the paths is given by 86 square metres.
96 square metres
76 square metres
126 square metres
20 metres

Q 2: The length and width of a rectangular plot are 30 m and 25 m respectively. Two rectangular paths of same width run inside the plot, one parallel to the length of the plot and the other parallel to its width. Find the width of the paths if the total area occupied by the paths is 204 square metres.
1 metre
3 metres
4 metres
5 metres

Q 3: The length and width of a rectangular plot are 25 m and 23 m respectively. Two rectangular paths each 3 m wide run inside the plot, one parallel to the length of the plot and the other parallel to its width. Find the total area occupied by the paths.
164 square metres
264 square metres
235 square metres
135 square metres

Q 4: The length and width of a rectangular plot are 28 m and 15 m respectively. Two rectangular paths each 4 m wide run inside the plot, one parallel to the length of the plot and the other parallel to its width. Find the total area occupied by the paths.
164 square metres
156 square metres
98 square metres
256 square metres

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Question 6: This question is available to subscribers only!


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