Word Problems On Area For Class 6th, 7th , 8th , 9th .
Q 1 ] . What is the cost of tiling a rectangle plot of land 1/2Km long and 200m wide at the rate of
Rs. 9 per hundred sq. m ? .
SOLUTION : Rectangular Plot
Given : Length = L = 1/2 Km = 500m
Wide = Breadth = B = 200m
Rate = Rs 9 per hundred sq. m.
Find cost of tiling = ?
Step 1 ] – Area of rectangle = L * B
A = 500 * 200 = 100000 sq. m .
Step 2 ] – Cost of tiling per 100 sq m = Rs . 9
Cost of tiling per 100000 sq. m = ?
Cost of tiling per 100000 sq. m = (100000 * 9 )/ 100 = Rs . 9000
ANS = The cost tiling the rectangular plot = Rs 9000
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Q 2] . A floor is 6m long and 5 m wide . A square carpet of side 4m is laid on the floor . Find the
area of the floor that is not carpeted .
SOLUTION :
Step 1 ] – FLOOR (rectangle )
Given : – Long = Length = L = 6m
Wide = Breadth = B = 5m
Area of Floor (rectangle ) = L * B
A = 6 * 5
Thus , A = 30 m2
Step 2 ] – Carpet ( square)
Side = 4m
Area of Carpet ( square) = S * S
A = 4*4 = 16m2
Step 3 ]- Area of the floor that is not carpeted = Area of floor – Area of carpet
= 30 -16
= 14m2
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Q 3 ] . A wall to wall carpeting of a room measuring 8m by 6m is to be done . What length of
carpet is just enough if the roll of carpet is 3m wide ?
SOLUTION :
Step 1 ] – ROOM (rectangle )
Length = L = 8m
Breadth = B = 6m
Area of Room = Area of carpet
Area of Room = L * B
= 8 * 6 = 48 m2
Step 2 ] – Carpet ( Rectangle )
Length = ?
Wide = B = 3m
Area of Carpet = Area of Room
Area of Carpet = 48m2
48 = L * B
48 = L * 3
48 / 3 = L
16 m = L
ANS – The length of carpet = 16m .
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Q 4 ] . A tablecloth measure 3m by 2m 50cm . Another table cloth measures 5m by 1m 50 cm .
Which rectangular table clothes costs more if they are made of the same cloth ?
SOLUTION :
1st Table cloth ( rectangle )
L = Length = 3m
B = Breadth = 2m 50cm = 2.50m
Area of 1st Table cloth = ?
A = L * B
A = 3 * 2.50 = 7.5 m2
2nd Table cloth ( rectangle )
L = 5m
B = 1m 50cm = 1.50cm
Area of 2nd table cloth = ?
A = L * B
A = 5 * 1.50 = 7.5m2
Since both the table cloth have equal area , their costs will also be same .
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Q 5 ]. A room measuring 7m by 6m is to be covered by square tiles of side 50cm . Find the
number of tiles required to cover the floor . If the cost of one tile is Rs. 60 . Find the cost of
tiles ?
SOLUTION :
Step 1] – Room ( floor )
L = 7m
B = 6m
Area of floor = ?
A =L * B
A = 7 * 6
A = 42 m2
Step 3 ] – Find number of tiles = ?
Cost of tiles = ?
Number of tiles = Area of floor
—————–
Area of each tile
= 42
——-
0.2500
= 168 tiles
Step 2 ] – Tiles ( square )
Sides = 50cm
= 0.50cm
Area of square = ?
A = S * S
A = 0.50 * 0.50
A = 0.2500 m2
Step 4] – Cost of 1 tile = Rs 60
Cost of 168 tiles = ?
Cost of 168 tiles = 168 * 60 = Rs 10,080
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Q 6 ] . The cost of cultivating a rectangular field at the rate of Rs 3 per m2 is Rs 1,728 . If the
breadth of the field is 18 m , find the cost of fencing the field at Rs 8.5 per meter .
SOLUTION :
Rectangular field
GIVEN : Total cost of cultivating = Rs 1728
Rate per sq meter = Rs 3
Breadth = B = 18m
Rate of fencing = Rs 8.5 per m
Find cost of fencing = ?
To find : Cost of fencing = P * R
We don’t know the perimeter
To find perimeter we don’t know the length .
Step 1] – To find length = ?
per sq meter = cost = Rs . 3
thus , how much sq meter ( area) = cost = Rs 1728
i .e . Area = 1728 / 3 =576 sq m
Step 2] –
A = L * B
576 = L * 18
Thus , L = 576 / 18
L = 32m
Step 3] – P = 2 * ( L + B )
P = 2 * ( 32 + 18 )
P = 2 * ( 50 )
P = 100 m
Step 4 ] – The cost of fencing = P * R
= 100 * 8.5 = Rs 850
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Q 7 ] . Four square flower beds each of side 1m are dug on a piece of land 7m long and 5m wide .
What is the area of remaining part of the land ?
SOLUTION :
Step 1 ] – Rectangular land
Given = L = Length = 7m
B = Breadth = 5m
Area of land = 7 * 5
= 35 m2
Step 2] – Square flower beds
Side = 1m
Number of flower beds = 4
Area of 1 flower bed = S * S = 1 * 1
A = 1 m2
Thus , Area of 4 flower beds = 4 * 1
= 4 m2
Step 3] – Area of remaining part of land = Area of rectangle – Area of 4 flower beds
= 35 – 4
= 31 m2
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Q 8 ] . How many tiles whose length and breadth are 12cm and 5cm respectively will needed to
fit in a rectangular region . Whose length and breadth are respectively .
a ] 200 cm and 144 cm
b ] 80cm and 48cm
SOLUTION : [a]
a ] Rectangular region
Step 1] – Length = L = 200cm
Breadth = B = 144 cm
Area = L * B
A = 200 * 144
A = 28800cm2
Step 2 ] – Rectangular tile
Length = L = 12cm
Breadth = B = 5cm
Area = L * B
A = 12 * 5
A = 60cm2
Step 3] – Number of tiles = Area of region 28800
——————- = ———— = 480 tiles
Area of each tile 60
ANS – Number of tiles is 480 .
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SOLUTION : [b]
b ] Rectangular region
Length = L = 80 cm
Breadth = B = 48 cm
Area = L * B
A = 80 * 48
A = 3840cm2
Step 2] – Rectangular tile
L = 12cm
B = 5cm
A = L * B
A = 12 * 5
A = 60 cm2
Step 3 ] –
Number of tiles = Area of rectangular region / Area of each tile = 3840 /60 = 64 tiles
ANS – Number of tiles required is = 64 .
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