Question

Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag the item to the trashcan. Click the trashcan to clear all your answers.

Find the area of a regular hexagon with the given measurement.

6-inch radius

A = sq. in.

Answer 1

The area of a regular hexagon with a 6-inch radius is approximately 93.53 square inches, calculated using the formula A = (3√3/2)r² for the area of a regular polygon.

Step-by-step explanation:

To find the area of a regular hexagon with a given 6-inch radius, we can use the formula for the area of a polygon: A = (3√3/2)r², where r is the radius. A regular hexagon can be divided into six equilateral triangles, and this formula is derived from the area of these triangles.

Plugging the given radius into the formula, we have:

A = (3√3/2)(6 in)² = (3√3/2)(36 in²) = 54√3 in²

To compute the exact decimal value of 54√3, you can use a calculator, which will yield: A ≈ 93.53 in²

Therefore, the area of the hexagon is approximately 93.53 square inches.