Question

The regular hexagon has a radius of 4 in. What is the approximate area of the hexagon?
24 in.2
42 in.2
48 in.2
84 in.2

Answer 1

The approximate area of the hexagon is 42 in²

Step-by-step explanation:

In a regular hexagon, the center angle is 60° in which dividing the angle, we get 30°.

Now, sin 30 = (Opposite side)/4

⇒ Opposite side = 2 inches

Now, the length of one side is 4 inches.

The apothem is given as:

r = √3/2 × a

Now, the area is given as:

A = 0.5 × a × P

Where,

a is apothem

P is perimeter

On substituting the values, we get,

A = 0.5(2 × √3)(4 × 6)

A = 24√3

∴ A = 41.57 in² ≈ 42 in²