Find the area, A of the region between the sides of a regular polygon with 6 sides inscribed inside a circle and the circle. The circle has a radius of 5 inches. Round your answer to two decimal places of accuracy.

Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Find the area, A of the region between the sides of a regular polygon with 6 sides inscribed inside a circle and the circle. The circle has a radius of 5 inches. Round your answer to two decimal places of accuracy.

Expert Solution
Step 1

Consider a regular hexagon ABCDEF that is regular polygon with 6 sides which is inscribed in the circle with the radius of 5 inches.

Draw the figure of the hexagon ABCDEF inscribed inside a circle.

Algebra homework question answer, step 1, image 1

It can be seen from the Figure that there are six triangle.

In AOB.

Find AOB.

AOB=360°60°=60°

The central angle is 60°.

Therefore, there are six equilateral triangle.

The radius of the circle is 5 inches.

Find the area of the circle.

A=πr2=π52=25π=78.54inches2

 

 

 

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