Answered

At Westonci.ca, we connect you with the answers you need, thanks to our active and informed community. Discover precise answers to your questions from a wide range of experts on our user-friendly Q&A platform. Discover in-depth answers to your questions from a wide network of professionals on our user-friendly Q&A platform.

Find the area of a regular hexagon with an apothem of 12 centimeters.

Sagot :

reedemily20011

Answer:

To find the area of a regular hexagon with an apothem of 12 centimeters, we can use the formula:

Area = 1/2 * Perimeter * Apothem

In a regular hexagon, each interior angle measures 120 degrees, and the apothem is the distance from the center of the hexagon to the midpoint of a side, forming a right angle with that side.

Given that the apothem is 12 centimeters, and in a regular hexagon, the apothem is also the height of each equilateral triangle formed within the hexagon, we can find the side length of the hexagon using trigonometry:

The apothem divides the equilateral triangle into two right-angled triangles. The height (apothem) is 12 cm, and the base (side of the hexagon) is the hypotenuse of one of these right-angled triangles.

Using trigonometry (sin 60° = opposite/hypotenuse), we can find the side length:

sin 60° = 12 / side length

side length = 12 / sin 60°

side length = 12 / √3 / 2

side length = 12 * 2 / √3

side length = 24 / √3

side length = 24√3 / 3

side length = 8√3

Now, we can calculate the perimeter of the hexagon:

Perimeter = 6 * side length

Perimeter = 6 * 8√3

Perimeter = 48√3

Finally, we can find the area using the formula:

Area = 1/2 * Perimeter * Apothem

Area = 1/2 * 48√3 * 12

Area = 24 * 12√3

Area = 288√3 square centimeters

Therefore, the area of the regular hexagon with an apothem of 12 centimeters is 288√3 square centimeters.

We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. Thanks for using our service. We're always here to provide accurate and up-to-date answers to all your queries. Thank you for trusting Westonci.ca. Don't forget to revisit us for more accurate and insightful answers.