A Rectangular plot of land 90 m by 50 m is divided into four equal parts by two cross paths 3.5 m wide. Find the area of cross paths and area of remaining portion?

The correct answer is: Final Answer:- ∴ Area of cross paths & area of the remaining portion are 477.75 m2 & 4,022.25 m2.

Step-by-step solution:-
In the adjacent figure-
Length of the outer rectangle = 90 m
Breadth of the outer rectangle = 50 m
Area of the outer rectangle = length × breadth
∴  Area of the outer rectangle = 90 × 50
∴  Area of the outer rectangle = 4,500 m² ............................................................................... (Equation i)
A. From the adjacent diagram, to find the Area of the cross paths, we need to find the Sum of Areas of vertical & Horizontal sections.
However, intersection of the 2 paths i.e. the blue portion in the given diagram is included in both the paths.
Hence, this will lead to double counting of the blue section.
To nullify this duplication, we need to first calculate the sum of the areas of 2 paths and subsequently, subtract the area of the blue portion once.
∴ Area of both the cross paths = Area of vertical section + Area of Horizontal section - Area of blue section ....................... (Equation ii)
Now, dimensions of the verical section are 50 m & 3.5 m
dimensions of the horizontal section are 90 m & 3.5 m
& dimensions of the blue section are 3.5 m & 3.5 m
Also, Area of a rectangle = length × breadth
Substituting these values in Equation ii, we get-
∴ Area of both the cross paths = Area of vertical section + Area of Horizontal section - Area of blue section
∴ Area of both the cross paths = 50 × 3.5 + 90 × 3.5 - 3.5 × 3.5
∴ Area of both the cross paths = 175 + 315 - 12.25
∴ Area of both the cross paths = 477.75 m2............................................................................... (Equation iii)
B. Area of the remaining portion = Area of the field - Area of the path
∴ Area of the remaining portion = 4,500 - 477.75 .......................................................................... (From Equations i & iii)
∴ Area of the remaining portion = 4,022.25 m²
Final Answer:-
∴ Area of cross paths & area of the remaining portion are 477.75 m² & 4,022.25 m².