8. Circular pathways

Circular pathways

Area pathways

The fundamental idea about the area of pathways

• We should observe the circular shapes around us where we need to find the area of the pathway.
• The area of the pathway is the difference between the area of the outer circle and inner circle.
• Let ‘R’ be the radius of the outer circle, and ‘r’ be the radius of the inner circle.

Therefore, the area of the circular pathway,
= πR² − πr² = π(R²−r²)sq.units
The circle is a round plane figure whose boundary (the circumference) consists of points equidistant from the fixed point (the centre). 
Area of the circle is the region enclosed by the circle.
Distance around the circular region is called the circumference or perimeter of the circle.
Area of the circle is πr² 
Here r is the radius of the circle.
Circumference of the circleis 2πr 
Here r is the radius of the circle. 

Rectangle pathways

The area of the rectangular pathway = Area of the outer rectangle – Area of the inner rectangle
The area of the rectangular pathway is (LB−lb) sq.units
The uniform path, including the park, is also a rectangle. If we consider the path as the outer rectangle, then the park will be the inner rectangle.
Let land b be the length and breadth of the park.
Area of the park (inner rectangle) = l × b  sq. units.
Let w be the width of the path. If L, B are the length and breadth of the outer rectangle, then
L =L + 2w and b=B + 2w.
Similarly for inner rectangle l=L−2wand b=B−2w