a rectangular lawn 100 m long and 70 m broad has two crossroads running in the middle of it - one 2m wide running parallel to its length and the other 5m wide running parallel to its breadth. find the area of the lawn not covered by the crossroads.
Answers
The area of the lawn not covered by the crossroads is 6460 m².
Step-by-step explanation:
Step 1:
Dimensions of the rectangular lawn:
Length, L = 30 m
Breadth, B = 20 m
The width of the path parallel to its length is 2 m and that of the path parallel to its breadth is 5 m.
Referring to the figure attached below, we get
The area of the rectangle ABCD = Length * Breadth = 100 * 70 = 7000 m²
Area of the path parallel to its breadth IJLK = 70 * 5 = 350 m²
Area of the path parallel to its length EFGH = 100 * 2 = 200 m²
and,
Area of the middle common path MNPO = 5 * 2 = 10 m²
Step 2:
∴ Area of the path is given by,
= [Area of the path parallel to its breadth IJLK] + [Area of the path parallel to its length EFGH] - [Area of the middle common path MNOP]
= 350 + 200 - 10
= 540 m²
Thus,
The area of the remaining portion is given by,
= [The area of the rectangle ABCD] - [Area of the paths]
= 7000 - 540
= 6460 m²
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Answer:
the common path must be subtracter
