Perimeter and Area | IT

Question 16

Below is the house plan of Charan. It is in a rectangular plot. Look at the plan. What do you notice?

Some of the measurements are given.

a. Find the missing measurements.

b. Find out the area of his house.

Question diagram 1
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Solution
Understand the Question
  • The house plan is on a rectangular plot with a total height of 30 ft30\text{ ft}.
  • Opposite sides of a rectangle are equal. We can find the total plot width by adding the widths of the sections aligned along the top edge: Master Bedroom (15 ft)+Toilet (5 ft)+Kitchen (15 ft)=35 ft\text{Master Bedroom } (15\text{ ft}) + \text{Toilet } (5\text{ ft}) + \text{Kitchen } (15\text{ ft}) = 35\text{ ft}.
  • Using the formula Area=Length×Width\text{Area} = \text{Length} \times \text{Width} and aligning the adjoining room boundaries, we can determine each missing dimension and room area.

a. Find the missing measurements.

Step 1 · Find Total Plot Dimensions

Question diagram

Diagram 1

Total Height=30 ft\text{Total Height} = 30\text{ ft}

Total Width=15 ft+5 ft+15 ft=35 ft\text{Total Width} = 15\text{ ft} + 5\text{ ft} + 15\text{ ft} = 35\text{ ft}

Total plot dimensions=35 ft×30 ft\text{Total plot dimensions} = 35\text{ ft} \times 30\text{ ft}

Step 2 · Calculate Missing Measurements and Areas

Small Bedroom: Height=180 sq ft÷15 ft=12 ft\text{Height} = 180\text{ sq ft} \div 15\text{ ft} = 12\text{ ft} Dimensions=15 ft×12 ft\text{Dimensions} = 15\text{ ft} \times 12\text{ ft}

Utility: Width=15 ft\text{Width} = 15\text{ ft} Height=15 ft−12 ft=3 ft\text{Height} = 15\text{ ft} - 12\text{ ft} = 3\text{ ft} Area=15 ft×3 ft=45 sq ft\text{Area} = 15\text{ ft} \times 3\text{ ft} = 45\text{ sq ft}

Garden: Height=30 ft−(15 ft+12 ft)=30 ft−27 ft=3 ft\text{Height} = 30\text{ ft} - (15\text{ ft} + 12\text{ ft}) = 30\text{ ft} - 27\text{ ft} = 3\text{ ft} Width=20 ft\text{Width} = 20\text{ ft} Area=20 ft×3 ft=60 sq ft\text{Area} = 20\text{ ft} \times 3\text{ ft} = 60\text{ sq ft}

Parking: Height=3 ft\text{Height} = 3\text{ ft} Width=15 ft\text{Width} = 15\text{ ft} Area=15 ft×3 ft=45 sq ft\text{Area} = 15\text{ ft} \times 3\text{ ft} = 45\text{ sq ft}

Diagram 2

Hall: Total Plot Area=35 ft×30 ft=1050 sq ft\text{Total Plot Area} = 35\text{ ft} \times 30\text{ ft} = 1050\text{ sq ft}

Sum of all other section areas:

Sum of known areas=225+50+45+180+180+60+45=785 sq ft\begin{aligned} \text{Sum of known areas} &= 225 + 50 + 45 + 180 + 180 + 60 + 45 \\ &= 785\text{ sq ft} \end{aligned}

Area of Hall=1050 sq ft−785 sq ft=265 sq ft\text{Area of Hall} = 1050\text{ sq ft} - 785\text{ sq ft} = 265\text{ sq ft}

Answer

a. * Utility: 15 ft×3 ft15\text{ ft} \times 3\text{ ft}, Area=45 sq ft\text{Area} = 45\text{ sq ft}

  • Kitchen: 15 ft×12 ft15\text{ ft} \times 12\text{ ft}, Area=180 sq ft\text{Area} = 180\text{ sq ft}
  • Master Bedroom: 15 ft×15 ft15\text{ ft} \times 15\text{ ft}, Area=225 sq ft\text{Area} = 225\text{ sq ft}
  • Toilet: 5 ft×10 ft5\text{ ft} \times 10\text{ ft}, Area=50 sq ft\text{Area} = 50\text{ sq ft}
  • Small Bedroom: 15 ft×12 ft15\text{ ft} \times 12\text{ ft}, Area=180 sq ft\text{Area} = 180\text{ sq ft}
  • Garden: 20 ft×3 ft20\text{ ft} \times 3\text{ ft}, Area=60 sq ft\text{Area} = 60\text{ sq ft}
  • Parking: 15 ft×3 ft15\text{ ft} \times 3\text{ ft}, Area=45 sq ft\text{Area} = 45\text{ sq ft}
  • Hall: Area=265 sq ft\text{Area} = 265\text{ sq ft}

b. Find out the area of his house.

Step 1 · Calculate Total Area of the House

Using the total dimensions of the rectangular plot:

Area of the house=Total Width×Total Height=35 ft×30 ft=1050 sq ft\begin{aligned} \text{Area of the house} &= \text{Total Width} \times \text{Total Height} \\ &= 35\text{ ft} \times 30\text{ ft} \\ &= 1050\text{ sq ft} \end{aligned}
Answer

b. 1050 sq ft1050\text{ sq ft}

Common Mistakes
  • Dimension Alignment Error: Forgetting that opposite boundary lines of a rectangular plot must match in total length when finding missing heights or widths.
  • Incorrect Hall Area Calculation: Missing one of the surrounding room areas when subtracting from the total plot area to find the Hall's remaining area.

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