The regular pentagon shown has an apothem with a length of 2 centimeters. To the nearest tenth, what is the area of the regular pentagon in square cintimeters

11.8cm²

Step-by-step explanation:

The area of the regular pentagon is expressed as;

A = pa/2

p is the perimeter of the pentagon

a is the apothem

Since p = 5s

s is the side length, hence;

A = 5sa/2

Get the side length s;

central angle = 360/5

central angle = 72degrees

angle in the right angle triangle =72/2 = 36degrees

Using SOH CAH TOA

sin 36 = x/2

x = 2sin36

x = 1.1755

s = 2x

s = 2.35cm

Get the area

A = 5(2.35)(2)/2

A = 5(2.35)

A = 11.8cm²

Hence the area of the regular pentagon is 11.8cm²

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