Question

there are 4 flowers beds each 5 m by 4 m at the corners of a square with grass path 2m wide between them . find the total area of the grass. if the whole is surrounded by a gravel path 3 m wide find the area of the gravel path​

Answer 1

The total area of the grass is 40 m². If the whole area is surrounded by a gravel path of 3 m width then the area of the gravel path is 168 m².

Step-by-step explanation:

Step 1:

Length of flower bed = 5m

Breadth of the flower bed = 4m

So, Area of one flower bed = l * b = 5 * 4 = 20 m²

∴ Area of 4 flower beds = 4 * 20 = 80 m²

Step 2:

It is given that each flower bed has a 2 m wide path between them.  

So we have,

The length of the field = 5 + 5 + 2 = 12 m

The breadth of the field = 4 + 4 +2 = 10 m

∴ Area of the field excluding the gravel path = l * b = 12 * 10 = 120 m²

∴ The total area of the grass will be given by,

= [Area of the field] – [Area of the 4 flower beds]

= 120 – 80

= 40 m²

Step 3:

Also given that the field area is surrounded by a gravel path of 3 m width, so,

The length of the field with gravel path = [length of the field] + [length of the gravel path on both sides] = 12 + 3 + 3 = 18 m

And,

Breadth of the field with the gravel path = [breadth of the field] + [breadth of the gravel path on 2 sides] = 10 + 3 + 3 = 16 m

Now,

The area of the complete field with the gravel path = 18 * 16 = 288 m²

∴ Area of the gravel path is given by,

= [Area of the complete field with the gravel path] – [area of the field excluding the gravel path]

= 288 – 120

= 168 m²

Thus, the area of the grass is 40 m² and the area of the gravel path is 168 m².

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