Answered

Westonci.ca is your go-to source for answers, with a community ready to provide accurate and timely information. Explore comprehensive solutions to your questions from a wide range of professionals on our user-friendly platform. Our platform provides a seamless experience for finding reliable answers from a network of experienced professionals.

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.

Thank you for your visit. We are dedicated to helping you find the information you need, whenever you need it. Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. Thank you for trusting Westonci.ca. Don't forget to revisit us for more accurate and insightful answers.