Area, General Mathematics

Question: A rectangular lawn 55 m by 35 m has two roads each 4 m wide running in the middle of it, one parallel to length and the other parallel to breadth. The cost of gravelling the roads at 75 paise per sq. metre is :
A
`Rs. 270`

B
`Rs. 262.50`

C
`Rs. 258`

D
`Rs. 254.50`

Note: Area of cross roads` = (55 xx 4 + 35 xx 4 - 4 xx 4) m^2` `= 344 m^2` :. cost of gravelling`= Rs. (344 xx 75/100)` `= Rs. 258`
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Question: A rectangular field has dimensions 25 m by 15 m. Two mutually perpendicular passages, 2 m wide have been left in the central part. In rest of the fields, grass has bee grown. The area under the grass is :
A
`295 m^2`

B
`299 m^2`

C
`300 m^2`

D
`375 m^2`

Note: Area of cross roads` = (25 xx 2 + 15 xx 2 - 2 xx 2) m^2` `= 76 m^2` Area of the field` = (25 xx 15) m^2` `= 375 m^2` Area under grass` = (375 - 76) m^2` `= 299 m^2`
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Question: The ratio between the length and breadth of a rectangular field is 5 : 4. If the breadth is 20 m less than the length, the perimeter of the field is :
A
`260 m`

B
`280 m`

C
`360 m`

D
None

Note: Let length = 5x and breadth = 4x in mertres. Then, `5x - 4x = 20 => x = 20` :. Length` = 100 m & Breadth = 80 m.` :. Perimeter` = 2 (100 + 80) m = 360 m.`
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Question: The length and breadth of a rectangular piece of land are in the ratio of 5 : 4 : 3. The owner spent Rs. 3000 for surrounding it from all the sides at Rs. 7.50 per metre. The difference between its length and breadth is :
A
`50 m`

B
`100 m`

C
`150 m`

D
`200 m`

Note: Let length = 5x and breadth = 3x in metres. Then, perimeter `= 2 (5x + 3x)` metres = 16x metres. But, perimeter `= Total cost/Rate/m` ` = (3000 xx 2/15) m` `= 400 m.` `:. 16x = 400 or x = 25.` :. Diff. in length & breadth `= (5x - 3x) = 2x = 50 m.`
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Question: The length of a plot is four times its breadth. A play ground measuring 1200 sq.m. occupies one-third of the total area of the plot. What is the length of the plot ?
A
`20 m`

B
`30 m`

C
`60 m`

D
None

Note: Not available
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Question: The length of a rectangle is twice its breadth and one of its diagonals measure `10sqrt(5)` cm. The perimeter of the rectangle is :
A
`60 cm`

B
`50 cm`

C
`250 cm`

D
None

Note: Let breadth = x cm and length = 2x cm. Then, `x^2 + (2x)^2` `= (10sqrt(5)^2 or 5x^2` `= 500 or x^2` `= 100 or x = 10` :. perimeter` = 2 (2x + x) cm` `= 6x cm = 60 cm.`
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Question: If the side of a square is increased by 5 cm, the area increases by 165 sq. cm. The side of the square is :
A
`13 cm`

B
`14 cm`

C
`15 cm`

D
`12 cm`

Note: Let, original side = x cm. Then, `(x + 5)^2 - x^2` `= 165 => 10x` `= 140 or x = 14.` :. Side of the square` = 14 cm.`
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Question: The length of a rectangle is doubled while its breadth is halved. What is change in area ?
A
`50% increase`

B
`75% increase`

C
`37.5% increase`

D
No change

Note: Let,length = a & breadth = b. Then, area = ab. New length = 2a & New breadth` = b/2.` :. New Area` = (2a xx b/2) = ab = original area.` Thus, there is no change in area.
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Question: A hall 36 m long and 15 m broad is to be paved with stones, each measuring 6 dm by 5 dm. The number of stones required is :
A
`180`

B
`1800`

C
`18`

D
`18000`

Note: Area of the hall` = (3600 xx 1500) sq. cm.` Area of each stone` = (60 xx 50) sq. cm.` :. Number of stones` = ((3600 xx 1500)/(60 xx 50))` ` = 1800.`
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Question: A hall 36 m long and 15 m broad is to be paved with stones, each measuring 6 dm by 5 dm. The number of stones required is :
A
`180`

B
`1800`

C
`18`

D
`18000`

Note: Area of the hall` = (3600 xx 1500) sq. cm.` Area of each stone` = (60 xx 50) sq. cm.` :. Number of stones` = ((3600 xx 1500)/(60 xx 50))` ` = 1800.`
1. Report

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Question: A rectangular lawn 55 m by 35 m has two roads each 4 m wide running in the middle of it, one parallel to length and the other parallel to breadth. The cost of gravelling the roads at 75 paise per sq. metre is :

Question: A rectangular field has dimensions 25 m by 15 m. Two mutually perpendicular passages, 2 m wide have been left in the central part. In rest of the fields, grass has bee grown. The area under the grass is :

Question: The ratio between the length and breadth of a rectangular field is 5 : 4. If the breadth is 20 m less than the length, the perimeter of the field is :

Question: The length and breadth of a rectangular piece of land are in the ratio of 5 : 4 : 3. The owner spent Rs. 3000 for surrounding it from all the sides at Rs. 7.50 per metre. The difference between its length and breadth is :

Question: The length of a plot is four times its breadth. A play ground measuring 1200 sq.m. occupies one-third of the total area of the plot. What is the length of the plot ?

Question: The length of a rectangle is twice its breadth and one of its diagonals measure `10sqrt(5)` cm. The perimeter of the rectangle is :

Question: If the side of a square is increased by 5 cm, the area increases by 165 sq. cm. The side of the square is :

Question: The length of a rectangle is doubled while its breadth is halved. What is change in area ?

Question: A hall 36 m long and 15 m broad is to be paved with stones, each measuring 6 dm by 5 dm. The number of stones required is :

Question: A hall 36 m long and 15 m broad is to be paved with stones, each measuring 6 dm by 5 dm. The number of stones required is :