Question

Architects design many types of buildings. They draw plans for houses, such as the plan shown in Fig:
An architect wants to install a decorative moulding around the ceilings in all the rooms. The decorative moulding cost of Rs. $$500/metre$$.
(a) Find how much moulding will be needed for each (i) family room (ii) living room (Hi) dining room (iv) bedroom $$1$$(v) bedroom $$2$$
(b) The carpet costs Rs. $$200/m^2$$. Find the cost of carpeting each room.
(c) What is the total cost of moulding for all the five rooms?

Answer 1

(a) (i) Perimeter of family room $$=2 (Length + breath)$$

Given, length $$= 5.48\, m$$ and breadth $$=4.57\, m$$

By Putting these values in above formula, we get

$$=2 \times (5.48+ 4.57) = 2 \times 10.05 = 20.10\, m$$

ii. Perimeter of living room $$= 2(length + breath)$$

Give, length $$=3.81\, m$$ and breadth$$= 7.53\, m$$

By purring these values in above formula, we get

$$=2\times (3.81 + 7.53) = 2 \times 11.34 = 22.68\, m$$

iii. Perimeter of dining room $$= 2(length + breath)$$

Given, length $$= 5.41 \,m$$ and breadth $$= 5.48\, M$$

By putting these values in above formula, we get

$$=2\times (5.41 + 5.48) = 2 \times 10.89 = 21.78\, m$$

iv. Perimeter of bedroom $$1= 2(length + breath)$$

Give, length $$= 3.04\, m$$ and breadth $$= 3.04\, m$$

By putting these values in above formula, we get

$$ =2 \times (3.04 + 3.04)=2 \times 6.08 = 12.16\, m$$

v. Perimeter of bedroom $$2 = 2(leng. + breath)$$

Given, length $$= 3.04\,m$$ and breadth $$= 2.43\, m$$

By putting these values in above formula, we get

$$= 2 \times (3.04+ 2.43)= 2 \times 5.47 = 10.94\, m$$

(b) For bedroom 1,

Given, length of bedroom $$1=304\, m$$ and death of bedroom $$1=304\, m$$ Area of bedroom $$1= 304\times 304 = 9.2416 \, sq \,m

\, Length \times Breadth$$

Area of bedroom $$1=304 \times 304 = 9.2416$$ sq m

Cost of carpeting $$1$$ sq m $$= Rs.\, 200$$

Cost of carpeting $$9.2416\, m^2= 9.2416 \times 200 = Rs. \,1848$$

For bedroom 2,

Given, length of bedroom $$2 = 304\, m$$ and breadth of bedroom $$2 = 243\, m$$

Area of bedroom $$2= Length \times Breadth$$

$$ = 304\times 2.43 = 7.3872\, m^2$$

Cost of carpeting $$1\, m^2 = Rs. 200$$

Cost of carpeting of living room $$1 \,m^2 = 200$$

Cost of carpeting $$ 7.3872\, m^2= 7.3872 \times 200 = Rs. 1477$$ for living room,

Given, length of living room $$= 3.81\times 7.53=28.6893\, m^2$$

Cost of carpeting of living room $$1\, m^2= Rs. 200$$

Cost of carpeting $$28.6893\, m^2 = Rs. 200\times 286893$$

$$=Rs. 5737.86$$

For dining room,

Given, length of dining room $$= 5.41\,m$$ and breadth of dining room $$= 5.48\, m$$

Area of dining room $$= 5.41\times 5.48=29.6468\, m^2$$

Cost of carpeting $$1\,m^2 = Rs.\, 200$$

Cost of carpeting $$28.6468 \,m^2= 29.5468 \times 200$$

$$=Rs. \,5929.36$$

For family room,

Given, length of family room $$=4.57\, m$$

Breadth of room $$= 5.48\, m$$

Area of family room $$ =5.48\times 4.57 =5.0436 \, m$$

Therefore cost of carpeting family room

$$= 25.0436\times 200 = Rs.\,5008.72$$

(c) Total perimeter of all the five rooms, $$=20.10\, m+22.68\, m+21.78\, m +12.16\, m +10.904\,m = 87.66\, m$$

Given, cost of moulding each room $$= Rs. 500$$ per m

Now, the total cost of moulding all $$5$$ rooms $$= 87.66 \times 500= Rs.\, 43830$$