Question
If you have a regular polygon with 11 sides and the sides are each 15 cm what is the area of the polygon the Apothem is roughly 11.99 cm
Ask by Kelley Robbins.
Feb 08,2025 02:52
Upstudy AI Solution
Tutor-Verified Answer
Answer
The area of the polygon is approximately 989.18 cm².
Solution
To find the area of a regular polygon, you can use the formula:
Area = (1/2) × (Perimeter) × (Apothem).
Step 1. Calculate the Perimeter.
Since there are 11 sides each 15 cm long:
Perimeter = 11 × 15 = 165 cm.
Step 2. Use the given Apothem.
Apothem ≈ 11.99 cm.
Step 3. Plug the values into the formula:
Area = 0.5 × 165 × 11.99.
Step 4. Perform the multiplication:
0.5 × 165 = 82.5,
82.5 × 11.99 ≈ 989.175 cm².
So, the area of the polygon is approximately 989.18 square centimeters.
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Simplify this solution Mind Expander
To find the area of an 11-sided polygon (hendecagon), you can use the formula: Area = (Perimeter × Apothem) / 2. With each side being 15 cm, the perimeter is 11 × 15 = 165 cm. Plugging that into the formula along with the apothem of approximately 11.99 cm gives you: Area = (165 × 11.99) / 2, which results in about 990.84 cm².
Fun fact: Regular polygons have been observed and admired since ancient times, with the Greeks particularly fascinated by their symmetry and aesthetic beauty. They believed that regular polygons, like the 11-sided figure, represented perfect forms in nature!
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