Respuesta :

luclaporte2

Answer:

A = 324.9

Step-by-step explanation:

We can determine the variables required to solve the area by using these three equations of a regular polygon:

  • a = s / 2 tan (180 / n) [Apothem/Inradius] [Tip: the radius is the same but with a sine instead of a tangent]
  • A = 1/2 (a)(p) [Area]
  • p = s * n [Perimeter]

We are given:

  • a = 10cm [Apothem]
  • n = 10 [# of sides]

We can rearrange the apothem equation to find s by multiplying both sides by the denominator on the right:

a = s / 2 tan (180 / n) [Apothem]

s = a * 2 tan (180 / n) [Reflexive property]

s = 10cm * 2 tan (18)

s ≈ 6.498 cm [The side length is approximately]

Now we have the info to find the perimeter using what we have gained:

p = s * n

p = (6.498) * (10)

p = 64.98 cm [This is the perimeter]

Finally we have enough information to solve for the area:

A = 1/2 * p * a

A = 1/2 * (64.98) * (10)

A = 1/2 * 649.8

A = 324.9 cm [Area of the decagon]

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