Question

Architects design many types of buildings. They draw plans for houses, such as the plan shown in the following figure:

An architect wants to install a decorative moulding around the ceilings in all the rooms. The decorative moulding costs ₹ 500/metre.

1. Find how much moulding will be needed for each room.
   (i) family room
   (ii) living room
   (iii) dining room
   (iv) bedroom 1
   (v) bedroom 2
2. The carpet costs ₹ 200/m². Find the cost of carpeting each room.
3. What is the total cost of moulding for all the five rooms.

Answer 1

a. (i) Given, breadth of the family room = 5.48 m

and length of the family room = 4.57 m

∴ Perimeter of the family room = 2(Length + Breadth)

= 2(5.48 + 4.57)

= 2 × 10.05

= 20.10 m

(ii) Given, length of the living room = 3.81 m

and breadth of the living room = 7.53 m

∴ Perimeter of the living room = 2(Length + Breadth)

= 2(3.81 + 7.53)

= 2 × 11.34

= 22.68 m

(iii) Given, breadth of the dining room = 5.48 m

and length of the dining room = 5.41 m

∴ Perimeter of the dining room = 2(Length + Breadth)

= 2(5.41 + 5.48)

= 2 × 10.89

= 21.78 m

(iv) Given, length of bedroom room 1 = 3.04 m

and breadth of bedroom 1 = 3.04 m

∴ Perimeter of the bedroom 1 = 2(Length + Breadth)

= 2(3.04 + 3.04)

= 2 × 6.08

= 12.16 m

(v) Given, breadth of bedroom 2 = 2.43 m

and length of bedroom 2 = 3.04 m

∴ Perimeter of the bedroom 2 = 2(Length + Breadth)

= 2(3.04 + 2.43)

= 2 × 5.47

= 10.94 m

b. For bedroom 1,

Given, length of bedroom 1 = 3.04 m

and breadth of bedroom 1 = 3.04 m

∴ Area of bedroom 1 = Length × Breadth

∴ Area of bedroom 1 = 3.04 × 3.04 = 9.2416 sq m

∵ Cost of carpeting 1 sq m = ₹ 200

∴ Cost of carpeting 9.2416 m² = 9.2416 × 200 = ₹ 1848

For bedroom 2,

Given, length of bedroom 2 = 3.04 m 

and breadth of bedroom 2 = 2.43 m

∴ Area of bedroom 2 = Length × Breadth

∴ Area of bedroom 2 = 3.04 × 2.43  = 7.3872 m²

∴ Cost of carpeting 1 m² = ₹ 200

∴ Cost of carpeting 7.3872 m² = 7.3872 × 200 = ₹ 1477

For living room,

Given, length of living room = 3.81 m

and breadth of living room = 7.53 m

∴ Area of living room = 3.81 × 7.53 = 28.6893 m²

∴ Cost of carpeting of living room 1 m² = ₹ 200

∴ Cost of carpeting 28.6893 m² = ₹ 200 × 28.6893 = ₹ 5737.86

For dining room,

Given, length of dining room = 5.41 m

and breadth of dining room = 5.48 m

∵  Area of dining room = 5.41 × 5.48 = 29.6468 m²

∵  Cost of carpeting 1 m² = ₹ 200

∴  Cost of carpeting 29.6468 m² = 29.6468 × 200 = ₹ 5929.36

For family room,

Given, length of family room = 4.57 m

and breadth of family room = 5.48 m

∴  Area of family room = 5.48 × 4.57 = 25.0436 m²

So, cost of carpeting family room = 25.0436 × 200 = ₹ 5008.72

c. Total perimeter of all the five rooms  = 20.10 m + 22.68 m + 21.78 m + 12.16 m + 10.94 m = 87.66 m

∵ Given, cost of moulding each room = ₹ 500 per m

∴ Total cost of moulding all five rooms = 87.66 × 500 = ₹ 43830