CLASS-7
MENSURATION - MORE EXAMPLES ON AREA OF PATHS
MORE WORK-OUT EXAMPLES ON AREA OF PATHS -
Examples.1) A rectangular lawn of length 50 m and breadth 35 m is to
be surrounded externally by a path which is 2 m
wide. Find the cost of turfing the path at the rate of $3 per m².
Ans.)
v Length of the lawn = 50 m
v Breadth of the lawn = 35 m
v Area of the lawn = (50 × 35) m²= 1750 m²
v Length of lawn including the path = [50 + (2 + 2)] m = 54 cm
v Breadth of the lawn including the path = [35 + (2 + 2)] m = 39 m
v Area of the lawn including the path = 54 × 39 m² = 2106 m²
v Therefore, area of the path = (2106 - 1750) m² = 356 m²
v For 1 m², the cost of turfing the path = $ 3
v For 356 m², the cost of turfing the path = $3 × 356 = $1068 (Ans.)
Example.2) A painting is painted on a cardboard 19 cm and 14 cm wide, such that there is a margin of 1.5 cm along each of its sides. Find the total area of the margin.
Ans.)
Length of the cardboard = 19 cm
v Breadth of the cardboard = 14 cm
v Area of the cardboard = 19 × 14 cm² = 266 cm²
v Length of the painting excluding the margin = [19 - (1.5 + 1.5)] cm
= 16 cm
v Breadth of the painting excluding the margin = 14 - (1.5 + 1.5) = 11 cm
v Area of the painting excluding the margin = (16 × 11) cm² = 176 cm²
v Therefore, area of the margin = (266 - 176) cm² = 90 cm² (Ans.)
Example.3) A square flowerbed is surrounded by a path 10 cm wide around it. If the area of the path is 2000 cm², find the area of the square flower-bed.
Ans.)
v ABCD is the square flowerbed.
v EFGH is the outer boundary of the path.
v Let each side of the flowerbed = x cm
v Then, the area of the square flowerbed ABCD (x × x) cm² = x² cm²
v Now, the side of the square EFGH = (x + 10 + 10) cm = (x + 20) cm
v So, the area of square EFGH = (x + 20) (x + 20) cm² = (x + 20)² cm²
v Therefore, area of the path = Area of EFGH - Area of ABCD
v = [(x + 20)² - x²] cm²
v = [x² + 400 + 40x - x²] cm²
= (40x + 400) cm²
v But the area of path given = 2000 cm²
v Therefore, 40x + 400 = 2000
v ⟹ 40x = 2000 - 400
v ⟹ 40x = 1600
v ⟹ x = 1600/40 = 40
v Therefore, side of square flowerbed = 40 cm
v Therefore, the area of the square flowerbed = 40 × 40 cm² = 1600 cm² (Ans.)
* To find out the cost of painting a board, covering a field with earth or tiling the floor/ flooring a room means to find out the area and then calculate the cost according to the rate given.
* To find out the cost of fencing or cost of giving a boundary means to find out the perimeter and then calculate the cost according to the rate given.
Example.4) Perimeter of the floor of the rectangular room is 17 m and its length is 5 m. Fine -
i) The breadth of the room
ii) The floor area of the room
iii) The cost of flooring the room with square tiles of side 25 cm at the rate of 85$ per hundred tiles.
Ans.) As per the given condition, perimeter of the floor of rectangular room is 17m and it's length (l) = 5m, we need to find out breadth (b)
So, As per the formulae, Perimeter = 2(l + b)
=> 17m = 2(5 + b)
=> 17m = 10 + 2b
=> 2b = 17m
=> b = 3.5m ...........(i) (Ans.)
As we know, the area of rectangle is = Length x breadth
= 5m x 3.5m
= 17.5 m².........(ii) (Ans.)
25cm = 0.25m
Area of the square tiles with one side 0.25m is = (side)² = (0.25m)² = 0.0625m²
now, we have to find how many tiles of 0.0625m²size is needed to cover rectanglar floor of size 17.5m²-
area of floor 17.5m²
------------------ = ----------- = 280 units
area of one tiles 0.0625m²
now, the cost of 100 tiles is 85$
85
cost of 1 tile is = --------
100
85
cost of 280 tiles = -------- x 280 = 238$..........(iii) (Ans.)
100