To solve the problem of finding the
area and
perimeter of the given floor plan, we will break it down into manageable steps. Let's start by analyzing the image and calculating the required values.
---
Step 1: Understand the Layout
The floor plan is divided into several rooms with labeled dimensions. The total dimensions of the entire floor plan are:
-
Length (horizontal): \( 9 \, \text{m} + 3 \, \text{m} + 3 \, \text{m} = 15 \, \text{m} \)
-
Width (vertical): \( 12 \, \text{m} + 3 \, \text{m} = 15 \, \text{m} \)
Thus, the entire floor plan is a square with side length \( 15 \, \text{m} \).
---
Step 2: Calculate the Total Area
The total area of the floor plan is:
\[
\text{Total Area} = \text{Length} \times \text{Width} = 15 \, \text{m} \times 15 \, \text{m} = 225 \, \text{m}^2
\]
---
Step 3: Calculate the Perimeter
The perimeter of the entire floor plan is:
\[
\text{Perimeter} = 4 \times \text{Side Length} = 4 \times 15 \, \text{m} = 60 \, \text{m}
\]
---
Step 4: Verify Individual Room Dimensions
Let's verify the dimensions of each room to ensure they fit within the total layout:
1.
Garden:
- Dimensions: \( 3 \, \text{m} \times 15 \, \text{m} \)
- Area: \( 3 \, \text{m} \times 15 \, \text{m} = 45 \, \text{m}^2 \)
2.
Living Room:
- Dimensions: \( 6 \, \text{m} \times 12 \, \text{m} \)
- Area: \( 6 \, \text{m} \times 12 \, \text{m} = 72 \, \text{m}^2 \)
3.
Kitchen:
- Dimensions: \( 3 \, \text{m} \times 7 \, \text{m} \)
- Area: \( 3 \, \text{m} \times 7 \, \text{m} = 21 \, \text{m}^2 \)
4.
Bedroom 1:
- Dimensions: \( 8 \, \text{m} \times 8 \, \text{m} \)
- Area: \( 8 \, \text{m} \times 8 \, \text{m} = 64 \, \text{m}^2 \)
5.
Bathroom 1:
- Dimensions: \( 3 \, \text{m} \times 7 \, \text{m} \)
- Area: \( 3 \, \text{m} \times 7 \, \text{m} = 21 \, \text{m}^2 \)
6.
Bedroom 2:
- Dimensions: \( 5 \, \text{m} \times 5 \, \text{m} \)
- Area: \( 5 \, \text{m} \times 5 \, \text{m} = 25 \, \text{m}^2 \)
7.
Balcony 1:
- Dimensions: \( 3 \, \text{m} \times 4 \, \text{m} \)
- Area: \( 3 \, \text{m} \times 4 \, \text{m} = 12 \, \text{m}^2 \)
8.
Balcony 2:
- Dimensions: \( 3 \, \text{m} \times 5 \, \text{m} \)
- Area: \( 3 \, \text{m} \times 5 \, \text{m} = 15 \, \text{m}^2 \)
9.
Bathroom 2:
- Dimensions: \( 6 \, \text{m} \times 3 \, \text{m} \)
- Area: \( 6 \, \text{m} \times 3 \, \text{m} = 18 \, \text{m}^2 \)
10.
Entrance:
- Dimensions: \( 3 \, \text{m} \times 3 \, \text{m} \)
- Area: \( 3 \, \text{m} \times 3 \, \text{m} = 9 \, \text{m}^2 \)
---
Step 5: Sum the Areas of All Rooms
To verify the total area, sum the areas of all individual rooms:
\[
\text{Total Area} = 45 + 72 + 21 + 64 + 21 + 25 + 12 + 15 + 18 + 9 = 225 \, \text{m}^2
\]
This matches the total area calculated earlier.
---
Final Answer
The total
area and
perimeter of the floor plan are:
\[
\boxed{225 \, \text{m}^2, 60 \, \text{m}}
\]
Parent Tip: Review the logic above to help your child master the concept of perimeter of a house worksheet.
