A room 12m by 10m has a carpet laid in the centre leaving 1m space all around. what is the area of th carpet and uncovered area?
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Given :
- Length of the room = 12 m
- Breadth of the room = 10 m
- A carpet is laid in the centre of the room leaving a space of 1 m all around.
To find :
- Area of the carpet
- Area uncovered by the carpet
Concept :
To find the area of the carpet :-
- Subtract (1 + 1)m from the dimensions of the room. The resultant values will be the dimensions of the carpet.
- By using the formula of area of rectangle, calculate the value of the area of carpet.
To find the uncovered area :-
- By using the formula of area of rectangle, calculate the area of the room.
- Subtract the area of carpet from the area of room, the resultant value will be the required answer.
Formula to calculate area of rectangle :-
- Area of rectangle = l × b
where,
- l stands for the length
- b stands for the breadth
Solution :
Dimensions of the carpet :-
→ Length of the carpet = 12 - (1 + 1) = 10 m
→ Breadth of the carpet = 10 - (1 + 1) = 8 m
Therefore,
- The dimensions of the carpet area 10 m by 8 m.
Finding the area of carpet :-
★ Area of carpet = l × b
Substituting the given values, we get :-
→ Area of carpet = 10 × 8
→ Area of carpet = 80
Therefore,
- The area of carpet = 80 m²
Now, calculating the area uncovered by the carpet :-
Area of the room :-
★ Area of room = l × b
Substituting the given values, we get :-
→ Area of room = 12 × 10
→ Area of room = 120
Therefore,
- Area of the room = 120 m²
The uncovered area = Area of the room - Area of carpet
→ Uncovered area = 120 - 80
→ Uncovered area = 40
Therefore,
- The uncovered area = 40 m²
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