Question
- The length of each side of a regular octagon is 10 cm . Find its area.
Ask by Hardy Rodriguez. in the United States
Mar 20,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The area of the regular octagon is approximately 482.84 cm².
Solution
To find the area of a regular octagon, we can use the formula for the area of a regular polygon:
where:
-
is the number of sides of the polygon (in this case, 8 for an octagon) -
is the length of each side of the polygon (in this case, 10 cm)
Substitute the values into the formula to find the area of the regular octagon.
The area of the regular octagon with each side length of 10 cm is approximately 482.84 cm².
The area of the regular octagon with each side length of 10 cm is approximately 482.84 cm².
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Simplify this solution Extra Insights
To find the area of a regular octagon, you can use the formula: Area = 2 * (1 + √2) * s², where s is the length of a side. With each side measuring 10 cm, the area calculates to approximately 200 cm². This formula is derived from simple geometric principles related to the properties of polygons and showcases the elegance of regular shapes!
Now let’s talk about real-world application. Regular octagons aren’t just academic exercises; they appear everywhere! Think of stop signs, which are shaped like octagons. Understanding their area can help in urban planning, design of road signs, or when figuring out the space needed for a circular garden path featuring octagonal tiles. It’s geometry in action!
