5 4 2 16 3 . There are 4 flower beds, each 5 m by 4 m, at the corners of a square with grass paths 2 m wide between them (compare with Fig. 16(c)]. Find the total area of the grass. If the whole flower bed is surrounded by a gravel path 3 m wide, find the area of the gravel path.
Answers
Answer:
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