Question

a rectangle lawn 100m long and 70m board has two crossroad 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 crossroad​

Answer 1

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Answer 2

$\: \: Given :-$

a rectangle lawn 100m long and 70m board has two crossroad 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 crossroad.

$\: \: Solution :-$

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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