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A regular hexagon is inscribed in a circle with a diameter of 8 inches.

a. What is the perimeter of the hexagon?

b. What is the area of the hexagon?

Step by step please!!!

A regular hexagon is inscribed in a circle with a diameter of 8 inches. a. What is-example-1
User Zanecola
by
2.6k points

1 Answer

22 votes
22 votes

Answer:

b) 41.6 square inches

Explanation:

A regular hexagon is inscribed in a circle with a diameter of 8 inches.

Step 1

We find the radius

Radius = Diameter/2

= 8 inches/2 = 4 inches

a. What is the perimeter of the hexagon?

b. What is the area of the hexagon?

An hexagon has 6 sides

The number of angles in an hexagon is calculated as:

[(Number of sides - 2) x 180]

= (6 - 2) x 180 = 720 ÷ 6 = 120°

The hexagon into 6 equilateral triangles with 4 for each of its sides.

The area of one of the triangles:

Height = 2√3

- one triangle's area = (1/2)bh = (1/2)(4)(2√3) = 4√3

The area of the hexagon by multiplying the one triangle's area by 6:

6 x 4√3 = 24√3 square inches

= 41.569219382 square inches

Approximately = 41.6 square inches

User BitsAndBytes
by
2.4k points
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