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Chapter 29: Chapter 29

Problem 557

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Find the area of a regular hexagon if one side has the length of 6

Short Answer

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The area of the regular hexagon is \(54\sqrt{3}\).
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TABLE OF CONTENTS :
TABLE OF CONTENTS

Step 1: Find the area of one equilateral triangle

To find the area of one equilateral triangle, we can use the formula: Area = (side length^2 * sqrt(3)) / 4 In this exercise, the side length is 6. Area = (6^2 * sqrt(3)) / 4 Area = (36 * sqrt(3)) / 4 Area = 9 * sqrt(3)

Step 2: Find the area of the hexagon

Now that we've found the area of one equilateral triangle, we can find the area of the hexagon by multiplying the area of one triangle by 6: Hexagon Area = 6 * (9 * sqrt(3)) Hexagon Area = 54 * sqrt(3) The area of the regular hexagon is 54 * sqrt(3).

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Most popular questions from this chapter

Chapter 29

Find the area of a regular hexagon inscribed in a circle of radius \(\mathrm{r}\). Calculate the area explicitly when a) \(\mathrm{r}=4\), b) \(\mathrm{r}=9\), c) \(\mathrm{r}=16\) d) \(\mathrm{r}=25\).
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Draw a circle with a circumscribed square. If the radius length of the circle is \(\mathrm{r}\), prove that the area of the square region is \(4 r^{2}\).
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Prove that the area bounded by a regular polygon of \(n\) sides circumscribed about a circle with a radius of length \(\mathrm{r}\) is given by the formula \(\mathrm{A}=\mathrm{nr}^{2} \tan \pi / \mathrm{n}\).
Chapter 29

Show that the area of a regular polygon equals one-half the product of the lengths of the apothem and the perimeter.
Chapter 29

Find the area of a regular hexagon circumscribed about a circle of radius \(\mathrm{r}\). Calculate the area explicitly if a) \(\mathrm{r}=4\); b) \(\mathrm{r}=9\) c) \(\mathrm{r}=16\) d) \(\mathrm{r}=25\).
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