Question

a playground 150 M long and 125 M wide has a pathway of with 10 M running breadthwise in the middle find the area of the pathway

Answer 1

Worked-out examples on Area of the Path: 

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. 



Solution: 

Length of the lawn = 50 m 

Breadth of the lawn = 35 m

Area of the lawn = (50 × 35) m²

                           = 1750 m²

Length of lawn including the path = [50 + (2 + 2)] m = 54 cm 

Breadth of the lawn including the path = [35 + (2 + 2)] m = 39 m 

Area of the lawn including the path = 54 × 39 m² = 2106 m² 

Therefore, area of the path = (2106 - 1750) m² = 356 m² 

For 1 m², the cost of turfing the path = $ 3 

For 356 m², the cost of turfing the path = $3 × 356 = $1068 




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. 

Solution:

Length of the cardboard = 19 cm 

Breadth of the cardboard = 14 cm

Area of the cardboard = 19 × 14 cm² = 266 cm² 

Length of the painting excluding the margin = [19 - (1.5 + 1.5)] cm = 16 cm 

Breadth of the painting excluding the margin = 14 - (1.5 + 1.5) = 11 cm 

Area of the painting excluding the margin = (16 × 11) cm² = 176 cm² 

Therefore, area of the margin = (266 - 176) cm² = 90 cm² 




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. 

Solution:

In the adjoining figure, 





ABCD is the square flowerbed. 

EFGH is the outer boundary of the path. 

Let each side of the flowerbed = x cm 

Then, the area of the square flowerbed ABCD (x × x) cm² = x² cm²

Now, the side of the square EFGH = (x + 10 + 10) cm = (x + 20) cm 

So, the area of square EFGH = (x + 20) (x + 20) cm² = (x + 20)² cm²

Therefore, area of the path = Area of EFGH - Area of ABCD

                                            = [(x + 20)² - x²] cm² 

                                            = [x² + 400 + 40x - x²] cm² = (40x + 400) cm²

But the area of path given = 2000 cm²

Therefore, 40x + 400 = 2000 

⟹ 40x = 2000 - 400 

⟹ 40x = 1600

⟹     x = 1600/40 = 40

Therefore, side of square flowerbed =40 cm 

Therefore, the area of the square flowerbed = 40 × 40 cm² = 1600 cm²

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