Question

A verandah 1.25 m wide is constructed all along the outside of a room 5.5 m long and 4 m wide ( I) Find the area of a verandah. ( ii) The cost of cementing the floor of verandah at ₹ 200 per m2​

Answer 1

(refer to the attachment)

Given :

A verandah 1.25 m wide is constructed all along the outside of a room 5.5 m long and 4 m wide.

To Find :

• Area of the verandah
• Cost of cementing the floor of verandah at ₹ 200 per m²

Solution :

Firstly, we have to find the area of the room. Then by adding the width of the verandah with both the length and breadth of the room we can get the area of the room along with the verandah. Now, by subtracting the area of the room along with the verandah from the area of the room we can get the area of the verandah. After that by multiplying the cost of cementing the floor per m² with the area of the verandah we will get the second answer.

Required Formula :

Area of rectangle = Length × Breadth

Explanation :

i)) Area of Verandah :

Area of room :

The room is in the form of a rectangle.

We have the dimensions of the room.

• Length = 5.5 m
• Breadth = 4 m

Area of rectangle = Length × Breadth

Substituting the values,

⇒ Area = 5.5 × 4

⇒ Area = 22

∴ Area = 22 m²

Area of the room is 22 m².

Area of room along with the verandah :

Length of the room along with verandah :

= 5.5 + 1.25 + 1.25

= 8 m

Breadth of the room along with verandah :

= 4 + 1.25 + 1.25

= 6.5 m

Now we got the dimensions.

• Length = 8 m
• Breadth = 6.5 m

Area of rectangle = Length × Breadth

Substituting the values,

⇒ Area = 8 × 6.5

⇒ Area = 52

∴ Area = 52 m²

Area of room along with the verandah is 52 m².

Now,

Area of verandah = Area of room along with the verandah - Area of the room

where,

• Area of room along with the verandah = 52 m²
• Area of the room = 22 m²

Substituting the values,

⇒ Area = 52 - 22

⇒ Area = 30

∴ Area = 30 m²

Area of the verandah is 30 m².

ii)) Cost of cementing :

Cost of cementing the floor of Verandah = Cost per m² × Area of verandah

where,

• Cost per m² = ₹ 200
• Area of the verandah = 30 m²

Substituting the values,

⇒ Cost = ₹ (200 × 30)

⇒ Cost = ₹ 6000

∴ Cost = ₹ 6,000.

Cost of cementing the floor of verandah is ₹ 6,000.