QQuestionMathematics
QuestionMathematics
Find the area of a regular octagon with an apothem of 2 cm.
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Step 1:I'll solve this problem step by step, following the specified LaTeX formatting guidelines:
Step 2:: Understand the Given Information
- Apothem (a) = 2 cm - For a regular octagon, we'll need to calculate the side length and use the area formula
Step 3:: Recall the Area Formula for a Regular Polygon
- $$a$$ = length of the apothem
The area of a regular polygon is given by the formula: Where:
Step 4:: Calculate the Side Length
s = 4 \tan\left(\frac{\pi}{8}\right)
s = 2a \times \tan\left(\frac{\pi}{n}\right)
Step 5:: Calculate the Side Length
\tan\left(\frac{\pi}{8}\right) \approx 0.414
s = 4 \times 0.414 = 1.656 \text{ cm}
Step 6:: Calculate the Area
A = \frac{1}{2} \times 8 \times 1.656 \times 2
A = 8 \times 1.656 = 13.248 \text{ cm}^{2}
Final Answer
The area of the regular octagon is 13.248 \text{ cm}^{2}.
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