Question

There are 4 flower beds, each 5m by 4m, at the corners of a square witb grass paths 2m wide between them. Find the total area of the grass. If the whole is surrounded by a gravel path 3m wide, find the area of the gravel path.​

Answer 1

The area of the grassy region is 40 sq m

Area of the region with the gravel path is 168 sq m

Step-by-step explanation:

Length of flower bed = 5m

Breadth of the flower bed = 4m

Area of one flower bed =l x b = 5 x 4 = 20 sq. m

Each flower bed has a 2 m path between them.  

So length of the garden = 5 m + 5 m +2 m = 12m

Breadth of the garden = 4m + 4m +2 m = 10m

Area of the garden = l x b = 12 x 10 = 120 sq m

The area of the grass region = Area of the garden – area of the 4 flower beds

            = 120 – (4 x 20)

   = 120- 80 = 40 sq m

Area of the grassy region is 40 sq m

The garden is surrounded by a gravel path which is 3 m wide

Thus, the length of the outer square = Length of the garden + length of the gravel path on both sides  

    = 12 m + 3 m + 3m

    = 18 m

Breadth of the region with the gravel path = Breadth of the garden square + breadth of the gravel path on 2 sides  

    = 10 m + 3m + 3m

    = 16 m

Thus, the area of the complete garden with the gravel path = 18 m x 16 m

       = 288sq m

Area of the region with the gravel path   = Area of the whole garden – area of the inner garden

         = 288sq m – 120 sq m

         = 168 sq m

Area of the gravel region is 168 sq m

Thus, the area of the grassy region is 40 sq m

Area of the region with the gravel path is 168 sq m