Answer :
Let's solve the problem of finding the area and perimeter of a square with a side length of [tex]\( 16 \frac{3}{4} \)[/tex] meters.
### Step 1: Convert the Mixed Number to an Improper Fraction
First, we need to convert [tex]\( 16 \frac{3}{4} \)[/tex] into an improper fraction or a decimal for easier calculation.
[tex]\[ 16 \frac{3}{4} = 16 + \frac{3}{4} \][/tex]
To convert this to a decimal:
[tex]\[ 16 \frac{3}{4} = 16 + 0.75 = 16.75 \][/tex]
### Step 2: Calculate the Area of the Square
The formula for the area [tex]\( A \)[/tex] of a square is:
[tex]\[ A = \text{side length}^2 \][/tex]
Substituting the side length:
[tex]\[ A = (16.75)^2 \][/tex]
After calculating:
[tex]\[ A = 280.5625 \, \text{m}^2 \][/tex]
### Step 3: Calculate the Perimeter of the Square
The formula for the perimeter [tex]\( P \)[/tex] of a square is:
[tex]\[ P = 4 \times \text{side length} \][/tex]
Substituting the side length:
[tex]\[ P = 4 \times 16.75 \][/tex]
After calculating:
[tex]\[ P = 67.0 \, \text{m} \][/tex]
### Final Answer
Therefore, the area of the square is [tex]\( 280.5625 \)[/tex] square meters, and the perimeter of the square is [tex]\( 67.0 \)[/tex] meters.
### Step 1: Convert the Mixed Number to an Improper Fraction
First, we need to convert [tex]\( 16 \frac{3}{4} \)[/tex] into an improper fraction or a decimal for easier calculation.
[tex]\[ 16 \frac{3}{4} = 16 + \frac{3}{4} \][/tex]
To convert this to a decimal:
[tex]\[ 16 \frac{3}{4} = 16 + 0.75 = 16.75 \][/tex]
### Step 2: Calculate the Area of the Square
The formula for the area [tex]\( A \)[/tex] of a square is:
[tex]\[ A = \text{side length}^2 \][/tex]
Substituting the side length:
[tex]\[ A = (16.75)^2 \][/tex]
After calculating:
[tex]\[ A = 280.5625 \, \text{m}^2 \][/tex]
### Step 3: Calculate the Perimeter of the Square
The formula for the perimeter [tex]\( P \)[/tex] of a square is:
[tex]\[ P = 4 \times \text{side length} \][/tex]
Substituting the side length:
[tex]\[ P = 4 \times 16.75 \][/tex]
After calculating:
[tex]\[ P = 67.0 \, \text{m} \][/tex]
### Final Answer
Therefore, the area of the square is [tex]\( 280.5625 \)[/tex] square meters, and the perimeter of the square is [tex]\( 67.0 \)[/tex] meters.
