The regular hexagon has a radius of 4 in. What is the approximate area of the hexagon?

Solution:

The central angle of a hexagon is 60 degrees

By dividing we get 30 degrees

sin 30 = opposite /4

Opposite = 2 inches

Given the length of one side is 4 inches

Apothem is r = √3/2 × a

Now, the area is given as:

A = 0.5 × a × P

Where,

a is apothem

P is perimeter

Substituting the values

A = 0.5(2 × √3)(4 × 6)

A = 24√3

A = 41.57 square inches

Therefore, the approximate area of the hexagon is 42 square inches.

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The regular hexagon has a radius of 4 in. What is the approximate area of the hexagon?

Summary:

The regular hexagon has a radius of 4 in. The approximate area of the hexagon is 42 square inches.