The length and breadth of rectangle field are 100meter and 60meter respectively. inside the field, a park of 10meter width is made around the field, the area of park is ?
Answers
Qᴜᴇsᴛɪᴏɴ :-
The length and breadth of rectangle field are 100meter and 60meter respectively. There is a park inside the field. A 10meter width path is built surrounding the park along the boundary of the park. Find the area of the park ?
Sᴏʟᴜᴛɪᴏɴ :-
- Length of the rectangular field = 100m
- Width of the path = 10m
- Breadth of the field = 60m
Length of the park = 100 - 2( 10 )
= 100 - 20
= 80m
Breadth of the park = 60 - 2( 10 )
= 60 - 20
= 40m
Area = Length × Breadth
= 80 × 40
= 3200
.°. Area of the park is 3200 m²
Correct Question :-
The length and breadth of rectangle field are 100meter and 60meter respectively. There is a Park inside the field. A 10 m wide path is built surrounding the Park along the boundary of the park. Find the area of the Park ?
Concept used :-
when Path is Inside The Rectangle :-
- Length of Park = Length of Rectangle - 2(Width of Path).
- Breadth of Park = Breadth of Rectangle - 2(Width of Path).
- Area of Park = Length * Breadth .
Sᴏʟᴜᴛɪᴏɴ :-
→ Length of Rectangle Field = 100m.
→ width of Path = 10m.
So,
→ Length of Park = Length of Rectangle - 2(Width of Path).
→ Length of Park = 100 - 2(10)
→ Length of Park = 100 - 20
→ Length of Park = 80m.
Similarly,
→ Breadth of Rectangle Field = 60m.
→ width of Path = 10m.
So,
→ Breadth of Park = Breadth of Rectangle - 2(Width of Path).
→ Breadth of Park = 60 - 2(10)
→ Breadth of Park = 60 - 20
→ Breadth of Park = 40m.
Therefore,
→ The Area of The Park = Length * Breadth .
→ Area of The Park = 80 * 40
→ Area of The Park = 3200m². (Ans.)
Hence, Area of Park inside Rectangle field is 3200m².
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Extra Tricks :-
→ Areas of path inside a rectangle :- (Length of Rect.+ Breadth of Rect. - 2*width of path) * (2*width of Path).
→ Areas of path Outside a rectangle :- (Length of Rect.+ Breadth of Rect. + 2*width of path) * (2*width of Path).
→ Area of path outside a square = (Side of Square + width of Path) * (4*width of Park).
→ Area of path inside a square = (Side of Square - width of Path) * (4*width of Park).
→ Area of Two paths of same width crossing each other perpendicularly inside a Rectangle = (width of Path) * ( Lenth of Rect. + Breadth of Rect. - width of Path ).
→ For Square , All Sides Are same , so , In This case Area will be = (width of Path) - (2*side of Square - width of Path).
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Now, in Question if Area of Path is Asked :-
→ Areas of path inside a rectangle :- (Length of Rect.+ Breadth of Rect. - 2*width of path) * (2*width of Path).
→ Areas of path inside rectangle = (100 + 60 - 2*10) * (2*10)
→ Areas of path inside rectangle = (100 + 60 - 20) * 20
→ Areas of path inside rectangle = 140 * 20
→ Areas of path inside rectangle = 2800 cm². (Ans.)