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Can anyone please explain? Need some help :)

A regular hexagon is inscribed in a circle with a diameter of 12 units. Find the area of the hexagon. Round your answer to the nearest tenth. (there's no picture included)

Can anyone please explain? Need some help :) A regular hexagon is inscribed in a circle-example-1
User Mote Zart
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1 Answer

5 votes

Answer:

93.5 square units

Explanation:

Diameter of the Circle = 12 Units

Therefore:

Radius of the Circle = 12/2 =6 Units

Since the hexagon is regular, it consists of 6 equilateral triangles of side length 6 units.

Area of the Hexagon = 6 X Area of one equilateral triangle

Area of an equilateral triangle of side length s =
(√(3) )/(4)s^2

Side Length, s=6 Units


\text{Therefore, the area of one equilateral triangle =}(√(3) )/(4)* 6^2\\\\=9√(3) $ square units

Area of the Hexagon


= 6 X 9√(3) \\=93.5$ square units (to the nearest tenth)

User Jacob Gillespie
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