Answer:
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
