Question

The diagram given below, shows two paths drawn inside a rectangular field 100 cm long and 55 cm wide. The width of two paths are 10 cm and 20 cm as shown. Find the area of the path.

• A. $1900{\text{cm}}^2$
• B. $2100{\text{cm}}^2$
• C. $2300{\text{cm}}^2$
• D. $2500{\text{cm}}^2$

Answer 1

The correct option is A

$1900{\text{cm}}^2$

Area(PQRS)=length $\times$ breadth $=20\times 10=200{\text{cm}}^2$

Area(EHIL)=length $\times$ breadth $=(100\times 10)=1000{\text{cm}}^2$

Area(FGJK)=length $\times$ breadth $=(55\times 20)=1100{\text{cm}}^2$

If we add area(EHIL) and area(FGJK); area(PQRS) will be counted twice. So, to find the exact area, we have to subtract area (PQRS) from the overall sum once.

$\therefore \text{Area of the path}=(1000+1100-200)=1900{\text{cm}}^2$