Question
Use the image to answer the question.
An illustration shows a hexagon with an inward triangle drawn from one of the sides. The triangle is marked A equals 4.
Find the area of the regular hexagon.
(1 point)
units
To find the area of the regular hexagon, we need to use the formula:
Area = 1/2 * apothem * perimeter.
The apothem can be found by dividing the equilateral triangle marked A equals 4 into two identical right triangles. Each right triangle will have a base of 2 and a height of 4. Using the Pythagorean theorem, we can find the length of the hypotenuse (which is the apothem) to be √(2² + 4²) = √20 = 2√5.
Now, the perimeter of the regular hexagon is 6 times the side length of each equilateral triangle, which is 6 times 4 = 24.
Plugging these values into the formula:
Area = 1/2 * 2√5 * 24 = 12√5 * 24 = 288√5 square units.
Therefore, the area of the regular hexagon is 288√5 square units.