Pregunta
Is this statement true or false? The area of a polygon with \( n \) sides, side length \( s \), and apothem \( a \) is \( A=\frac{1}{2} \) ans. false
Ask by Henry Ross. in the United States
Jan 23,2025
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The statement is false. The correct area formula for a regular polygon is \( A = \frac{1}{2} \times n \times s \times a \).
Solución
The statement is false.
The correct formula for the area \( A \) of a regular polygon with \( n \) sides, side length \( s \), and apothem \( a \) is given by:
\[
A = \frac{1}{2} \times n \times s \times a
\]
This means that the area is calculated as half the product of the number of sides, the side length, and the apothem. The statement you provided incorrectly states the formula as \( A = \frac{1}{2} \) ans, which is incomplete and does not represent the correct area formula for a polygon.
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Simplifique esta solución Extra Insights
The area of a regular polygon with \( n \) sides, side length \( s \), and apothem \( a \) is given by the formula \( A = \frac{1}{2} \times n \times s \times a \). So, while the general structure of the statement is on the right track, the term "ans" seems to be a typographical error, making the overall statement false. In practice, understanding how to find the area of polygons helps in architecture and engineering, where calculating space efficiently is essential. For example, when designing parks or buildings, knowing how to use the area formulas can help optimize land use and functionality, making spaces more enjoyable for the community.
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