To determine the perimeter and area of an equilateral triangle with each side measuring 6 feet, let's follow the steps involved.
### Step-by-Step Solution:
1. Perimeter Calculation:
The perimeter [tex]\( P \)[/tex] of an equilateral triangle is found by adding the lengths of all three sides. Since all sides are equal, the formula is:
[tex]\[
P = 3 \times \text{side length}
\][/tex]
Given the side length is 6 feet:
[tex]\[
P = 3 \times 6 = 18 \text{ feet}
\][/tex]
So, the perimeter of the equilateral triangle is 18 feet.
2. Area Calculation:
The area [tex]\( A \)[/tex] of an equilateral triangle can be calculated using the formula:
[tex]\[
A = \frac{\sqrt{3}}{4} \times \text{side length}^2
\][/tex]
Given the side length is 6 feet, we substitute into the formula:
[tex]\[
A = \frac{\sqrt{3}}{4} \times 6^2
\][/tex]
Calculating inside the parentheses first:
[tex]\[
6^2 = 36
\][/tex]
Now multiply:
[tex]\[
A = \frac{\sqrt{3}}{4} \times 36
\][/tex]
The value of [tex]\( \sqrt{3} \)[/tex] approximately equals 1.732. So,
[tex]\[
A \approx \frac{1.732}{4} \times 36
\][/tex]
Simplify the fraction first:
[tex]\[
\frac{1.732}{4} = 0.433
\][/tex]
Now multiply by 36:
[tex]\[
A \approx 0.433 \times 36 = 15.588
\][/tex]
So, the area of the equilateral triangle is approximately 15.588 square feet.
### Conclusion:
Given the above calculations:
- The perimeter of the equilateral triangle is [tex]\( 18 \)[/tex] feet.
- The area of the equilateral triangle is approximately [tex]\( 15.6 \)[/tex] square feet.
The correct answer is:
- Perimeter [tex]\(= 18 \, \text{ft}\)[/tex]
- Area [tex]\(= 15.6 \, \text{ft}^2\)[/tex]
