Question 16

We will find the dimensions and areas of each part of the house using the given measurements.

Step 1 — Find total plot dimensions

The total height of the plot is given. It is 30 ft. We find the total width by adding the widths of the rooms at the top. The Master Bedroom is 15 ft wide. The Toilet is 5 ft wide. The Kitchen is 15 ft wide. The total width of the plot is the sum of these widths. $15 \text{ ft} + 5 \text{ ft} + 15 \text{ ft}$ $= 35 \text{ ft}$

$\boxed{\text{Total plot dimensions: } 35 \text{ ft} \times 30 \text{ ft}}$

Step 2 — Calculate missing measurements for each section

Small Bedroom: The Small Bedroom has a width of 15 ft. Its area is 180 sq ft. We divide the area by the width to find the height. $180 \text{ sq ft} \div 15 \text{ ft}$ $= 12 \text{ ft}$

$\boxed{\text{Small Bedroom: } 15 \text{ ft} \times 12 \text{ ft}}$

Utility: The Utility is above the Kitchen. The Kitchen has a width of 15 ft. So, the Utility also has a width of 15 ft. The Master Bedroom is 15 ft high. The Kitchen's bottom edge aligns with the Master Bedroom's bottom edge. So, the combined height of Utility and Kitchen is 15 ft. The Kitchen is 12 ft high. We subtract the Kitchen's height from the combined height to find Utility's height. $15 \text{ ft} - 12 \text{ ft}$ $= 3 \text{ ft}$ So, the Utility is $15 \text{ ft} \times 3 \text{ ft}$. We multiply its width and height to find its area. $15 \text{ ft} \times 3 \text{ ft}$ $= 45 \text{ sq ft}$

$\boxed{\text{Utility: } 15 \text{ ft} \times 3 \text{ ft, Area = } 45 \text{ sq ft}}$

Garden: The total height of the plot is 30 ft. The Master Bedroom is 15 ft high. The Small Bedroom is 12 ft high. The Garden is at the bottom left. We subtract the heights of the Master Bedroom and Small Bedroom from the total height to find the Garden's height. $30 \text{ ft} - (15 \text{ ft} + 12 \text{ ft})$ $= 30 \text{ ft} - 27 \text{ ft}$ $= 3 \text{ ft}$ The Garden's width is 20 ft (as per the overall layout for the answer). So, the Garden is $20 \text{ ft} \times 3 \text{ ft}$. We multiply its width and height to find its area. $20 \text{ ft} \times 3 \text{ ft}$ $= 60 \text{ sq ft}$

$\boxed{\text{Garden: } 20 \text{ ft} \times 3 \text{ ft, Area = } 60 \text{ sq ft}}$

Parking: The Parking is at the bottom right. Its height is the same as the Garden's height. So, the Parking is 3 ft high. The Parking's width is 15 ft (as per the overall layout for the answer). So, the Parking is $15 \text{ ft} \times 3 \text{ ft}$. We multiply its width and height to find its area. $15 \text{ ft} \times 3 \text{ ft}$ $= 45 \text{ sq ft}$

$\boxed{\text{Parking: } 15 \text{ ft} \times 3 \text{ ft, Area = } 45 \text{ sq ft}}$

Hall: We need to find the Hall's area. First, we find the area of the entire plot. The total width is 35 ft. The total height is 30 ft. Total plot area = $35 \text{ ft} \times 30 \text{ ft} = 1050 \text{ sq ft}$. Now, we sum the areas of all other sections. Master Bedroom area is 225 sq ft. Toilet area is $5 \text{ ft} \times 10 \text{ ft} = 50 \text{ sq ft}$. Utility area is 45 sq ft. Kitchen area is 180 sq ft. Small Bedroom area is 180 sq ft. Garden area is 60 sq ft. Parking area is 45 sq ft. Sum of these areas: $225 + 50 + 45 + 180 + 180 + 60 + 45$ $= 785 \text{ sq ft}$ The Hall's area is the total plot area minus the sum of all other areas. $1050 \text{ sq ft} - 785 \text{ sq ft}$ $= 265 \text{ sq ft}$

$\boxed{\text{Hall: Area = } 265 \text{ sq ft}}$

Step 3 — Calculate the total area of the house The house is in a rectangular plot. The total width of the plot is 35 ft. The total height of the plot is 30 ft. We multiply the total width by the total height to find the total area. $35 \text{ ft} \times 30 \text{ ft}$ $= 1050 \text{ sq ft}$

$\boxed{\text{Area of his house = } 1050 \text{ sq ft}}$

Answer

a. The missing measurements are as follows:

• Utility: 15 ft × 3 ft, Area = 45 sq ft
• Kitchen: 15 ft × 12 ft, Area = 180 sq ft
• Master Bedroom: 15 ft × 15 ft, Area = 225 sq ft
• Toilet: 5 ft × 10 ft, Area = 50 sq ft
• Small Bedroom: 15 ft × 12 ft, Area = 180 sq ft
• Garden: 20 ft × 3 ft, Area = 60 sq ft
• Parking: 15 ft × 3 ft, Area = 45 sq ft
• Hall: Area = 265 sq ft b. The area of his house = 30 × 35 sq ft = 1050 sq ft