Question
Use the formula to determine the area of a regular pentagon with edges measuring 4.5 inches and an apothem measuring 6 inches
Answers
Answered by
GPT-4o mini
To calculate the area of a regular pentagon, you can use the following formula:
\[
\text{Area} = \frac{1}{2} \times \text{Perimeter} \times \text{Apothem}
\]
1. **Find the Perimeter**: The perimeter (P) of a regular pentagon can be calculated by multiplying the length of one side by the number of sides. Since each edge measures 4.5 inches and there are 5 sides in a pentagon:
\[
\text{Perimeter} = 5 \times 4.5 = 22.5 \text{ inches}
\]
2. **Use the Apothem**: The problem states that the apothem (a) is 6 inches.
3. **Calculate the Area**:
\[
\text{Area} = \frac{1}{2} \times \text{Perimeter} \times \text{Apothem} = \frac{1}{2} \times 22.5 \times 6
\]
\[
\text{Area} = \frac{1}{2} \times 135 = 67.5 \text{ square inches}
\]
Thus, the area of the regular pentagon is **67.5 square inches**.
\[
\text{Area} = \frac{1}{2} \times \text{Perimeter} \times \text{Apothem}
\]
1. **Find the Perimeter**: The perimeter (P) of a regular pentagon can be calculated by multiplying the length of one side by the number of sides. Since each edge measures 4.5 inches and there are 5 sides in a pentagon:
\[
\text{Perimeter} = 5 \times 4.5 = 22.5 \text{ inches}
\]
2. **Use the Apothem**: The problem states that the apothem (a) is 6 inches.
3. **Calculate the Area**:
\[
\text{Area} = \frac{1}{2} \times \text{Perimeter} \times \text{Apothem} = \frac{1}{2} \times 22.5 \times 6
\]
\[
\text{Area} = \frac{1}{2} \times 135 = 67.5 \text{ square inches}
\]
Thus, the area of the regular pentagon is **67.5 square inches**.
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