Answer :
To solve this problem, let's follow these steps:
1. Calculate the Perimeter of the Triangle:
The perimeter of a triangle is the sum of the lengths of its sides.
Given the sides are 4 units, 6 units, and 7.21 units, we can calculate the perimeter as follows:
[tex]\[ \text{Perimeter} = 4 + 6 + 7.21 = 17.21 \text{ units} \][/tex]
2. Determine the Circumference of the Circle:
According to the problem, the circumference of the circle is equal to the perimeter of the triangle. Therefore, the circumference is 17.21 units.
3. Calculate the Radius of the Circle:
The formula for the circumference of a circle is \( C = 2 \cdot \pi \cdot r \), where \( C \) is the circumference and \( r \) is the radius. We need to solve for \( r \).
[tex]\[ 17.21 = 2 \cdot 3.14 \cdot r \][/tex]
Dividing both sides by \( 2 \cdot 3.14 \):
[tex]\[ r = \frac{17.21}{2 \cdot 3.14} \approx 2.74 \text{ units} \][/tex]
4. Calculate the Area of the Circle:
The formula for the area of a circle is \( A = \pi \cdot r^2 \), where \( A \) is the area and \( r \) is the radius.
Substituting \( r = 2.74 \) units:
[tex]\[ A = 3.14 \cdot (2.74)^2 \][/tex]
Simplifying the equation:
[tex]\[ A = 3.14 \cdot 7.51 \approx 23.58 \text{ square units} \][/tex]
5. Round the Area to the Nearest Whole Number:
Rounding 23.58 to the nearest whole number, we get 24 square units.
Therefore, the area of the circle is 24 square units.
The correct answer is:
[tex]\[ \boxed{24 \text{ units}^2} \][/tex]
1. Calculate the Perimeter of the Triangle:
The perimeter of a triangle is the sum of the lengths of its sides.
Given the sides are 4 units, 6 units, and 7.21 units, we can calculate the perimeter as follows:
[tex]\[ \text{Perimeter} = 4 + 6 + 7.21 = 17.21 \text{ units} \][/tex]
2. Determine the Circumference of the Circle:
According to the problem, the circumference of the circle is equal to the perimeter of the triangle. Therefore, the circumference is 17.21 units.
3. Calculate the Radius of the Circle:
The formula for the circumference of a circle is \( C = 2 \cdot \pi \cdot r \), where \( C \) is the circumference and \( r \) is the radius. We need to solve for \( r \).
[tex]\[ 17.21 = 2 \cdot 3.14 \cdot r \][/tex]
Dividing both sides by \( 2 \cdot 3.14 \):
[tex]\[ r = \frac{17.21}{2 \cdot 3.14} \approx 2.74 \text{ units} \][/tex]
4. Calculate the Area of the Circle:
The formula for the area of a circle is \( A = \pi \cdot r^2 \), where \( A \) is the area and \( r \) is the radius.
Substituting \( r = 2.74 \) units:
[tex]\[ A = 3.14 \cdot (2.74)^2 \][/tex]
Simplifying the equation:
[tex]\[ A = 3.14 \cdot 7.51 \approx 23.58 \text{ square units} \][/tex]
5. Round the Area to the Nearest Whole Number:
Rounding 23.58 to the nearest whole number, we get 24 square units.
Therefore, the area of the circle is 24 square units.
The correct answer is:
[tex]\[ \boxed{24 \text{ units}^2} \][/tex]
