Using the Pythagorean theorem, we can calculate the apothem of the pentagon.
We have then:
[tex] a = \sqrt{12 ^ 2 - (\frac{14.1}{2}) ^ 2}
a = 9.7
[/tex]
Then, the area of the pentagon is given by:
[tex] A = 5 * (\frac{1}{2}) * (L) * (a)
[/tex]
Where,
L: side of the pentagon
a: apotema
Substituting values:
[tex] A = 5 * (\frac{1}{2}) * (14.1) * (9.7)
A = 341.925
[/tex]
Rounding the nearest whole we have:
[tex] A = 342 cm ^ 2
[/tex]
Answer:
the approximate area of the regular pentagon is:
[tex] A = 342 cm ^ 2
[/tex]
