1 Answer

Andbeonetraveler · Answer 1 · 2023-02-21T06:33:06+0000

2To find the area of each regular polygon, we have to use the following formula:

$A=(P\cdot a)/(2)$

Where P is the perimeter of the polygon and a is its apothem.

9. To find the area of this polygon, find its perimeter and its apothem.

To find its perimeter multiply the sidelength, 14cm, times the number of sides of the polygon:

$P=14cm\cdot9=126cm$

To find the apothem, we have to use the following formula:

$a=(l)/(2tan\theta)$

Where l is the sidelength and θ is half the central angle. Replace l for 14 and θ for 20:

Replace for these values and find the area:

$A=(126cm\cdot19.23cm)/(2)=1211.49cm^2$

10. To find the perimeter of this polygon we have to find its side length:

$l=2rsin\theta$

Where r is the radius and θ is half the central angle:

$\begin{gathered} l=2(6ft)sin36 \\ l=7.05ft \end{gathered}$

Find the perimeter by multiplying this sidelength by 5:

$P=7.05ft\cdot5=35.25ft$

Find the apothem using the same formula as in the other polygon:

Find the area using these values:

$A=(35.25ft\cdot4.85ft)/(2)=85.48ft^2$

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