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What is the area of a regular hexagon whose perimeter is 24 feet ?

User Mickfold
by
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2 Answers

1 vote

The formula for the area of a regular polygon is as follows:

A=1/2*a*P

A=area

a=apothem

P=perimeter

Before we can begin solving the problem, we have to determine the side lengths and apothem.

Side lengths=24/6=4

How can we find the apothem? Draw a diagram.

Note: the central angle of a regular hexagon is 60 degrees.

Since the triangle in the diagram is a 30-60-90 kind of one, the length of the long leg (a) = sqrt 3*short leg.

a=2 sqrt 3

Now we can calculate the area:

A=1/2*2 sqrt 3*24

A=41.5692194 or about 41.57

What is the area of a regular hexagon whose perimeter is 24 feet ?-example-1
User Vedburtruba
by
7.8k points
1 vote

Answer:

41.56922ft²

Explanation:

Using the formulas

P=6a

A=3sqrt3 /2 (a^2)

Solving forA

A=sqrt3P^2/24=

sqrt3*24^2/24

≈41.56922ft²

User Gboeing
by
7.8k points

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