Question

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?

Answer 1

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