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7. A square room is 12 ft long and 9 ft high. The room has 2 windows of size \( 4 \mathrm{ftx6ft} \) and a door of size \( 3 \mathrm{ft} \times 6 \mathrm{ft} \). एडटा वगांकार कोठा 12 फिट लामो छ मने 9 फिट आलो छ। यसमा 4 फिटx 6 फिटका 2 ओटा भटाल छन् भने 3 फिट \( x 6 \) फिटको एडटा ढोका छ। i) Find the area of 4 walls without door and windows. कयाल ढोका वाहेक चार भित्ताको क्षेत्रफल निकान्नुहोस् । [2] ii) How much does it cost to colour its ceiling and four walls with door and windows at the rate of Rs. 300 per square ft ? प्रति 10 वर्ग फिटको रु. 300 का दरले यसको भूयाल ढोका सहित चार भित्ता र सिलिडमा रड़ लगाउन जम्मा कति खर्च लाग्ध? [3]

Ask by Fleming Powell. in Nepal
Jan 26,2025

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**भाग (i):** ढोका र भटालहरू बाहेक चार भित्ताको कुल क्षेत्रफल **३६६ वर्ग फिट** छ। **भाग (ii):** भूयाल र चार भित्तामा रंग लगाउन **रु. १५,३००** खर्च लाग्नेछ।

Solution

### भाग (i): ढोका र भटालहरू बाहेक चार भित्ताको क्षेत्रफल **दीएको:** - कोठाको आकार: वर्गाकार (लामो: १२ फिट, चौडाइ: १२ फिट) - उचाइ: ९ फिट - भटालको आकार: प्रत्येक ४ फिट × ६ फिट (२ ओटा) - ढोकाको आकार: ३ फिट × ६ फिट **गणना:** 1. **चार भित्ताको कुल क्षेत्रफल:** \[ 4 \times (\text{लामो} \times \text{उचाइ}) = 4 \times (12 \, \text{फिट} \times 9 \, \text{फिट}) = 4 \times 108 = 432 \, \text{वर्ग फिट} \] 2. **भटाल र ढोकाको क्षेत्रफल:** \[ 2 \times (4 \times 6) + (3 \times 6) = 2 \times 24 + 18 = 48 + 18 = 66 \, \text{वर्ग फिट} \] 3. **ढोका र भटालहरू बाहेकको क्षेत्रफल:** \[ 432 - 66 = 366 \, \text{वर्ग फिट} \] **उत्तर:** चार भित्ताको क्षेत्रफल ढोका र भटालहरू बाहेक **३६६ वर्ग फिट** छ। --- ### भाग (ii): भूयाल र भित्तामा रंग लगाउने खर्च **दीएको:** - भूयालको क्षेत्रफल: १२ फिट × १२ फिट = १४४ वर्ग फिट - चार भित्ताको क्षेत्रफल (ढोका र भटालहरू बाहेक): ३६६ वर्ग फिट - कुल क्षेत्रफल: \[ १४४ + ३६६ = ५१० \, \text{वर्ग फिट} \] - रंगको दर: प्रति १० वर्ग फिटमा रु. ३०० **गणना:** \[ \frac{५१०}{१०} \times ३०० = ५१ \times ३०० = १५,३०० \, \text{रुपैयाँ} \] **उत्तर:** भूयाल र चार भित्तामा रंग लगाउन **रु. १५,३००** खर्च लाग्नेछ।

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To find the area of the four walls of the room, you first need to calculate the perimeter of the room and then multiply it by the height. The perimeter is \(4 \times 12 \, \text{ft} = 48 \, \text{ft}\). The area of the four walls is thus \(48 \, \text{ft} \times 9 \, \text{ft} = 432 \, \text{sq ft}\). Now, we subtract the areas of the windows and door. The total area of the windows is \(2 \times (4 \, \text{ft} \times 6 \, \text{ft}) = 48 \, \text{sq ft}\) and the area of the door is \(3 \, \text{ft} \times 6 \, \text{ft} = 18 \, \text{sq ft}\). Therefore, the area of the walls without door and windows is \(432 \, \text{sq ft} - (48 + 18) \, \text{sq ft} = 366 \, \text{sq ft}\). For the cost to color the ceiling and four walls including the door and windows, we first calculate the total area. The ceiling area is \(12 \, \text{ft} \times 12 \, \text{ft} = 144 \, \text{sq ft}\). Adding this to the wall area with windows and door gives us \(432 \, \text{sq ft}\). The total area to be colored is \(144 \, \text{sq ft} + 432 \, \text{sq ft} = 576 \, \text{sq ft}\). Since the cost is Rs. 300 per 10 sq ft, the total cost is \((576 \, \text{sq ft} ÷ 10) \times 300 = Rs. 17,280\). So, total area of walls without door and windows is \(366 \, \text{sq ft}\) and the total cost to color the ceiling and walls is \(Rs. 17,280\).

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