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Sagot :
Given:
Sum of all the interior angles of a regular polygon is 1080°.
Measure of each side is 10 cm.
To find:
The perimeter.
Solution:
The sum of all interior angles of a regular polygon with n side is:
[tex]S=(n-2)180^\circ[/tex]
Sum of all the interior angles of a regular polygon is 1080°.
[tex]1080^\circ=(n-2)180^\circ[/tex]
[tex]\dfrac{1080^\circ}{180^\circ}=n-2[/tex]
[tex]6+2=n[/tex]
[tex]8=n[/tex]
Number of sides of the regular polygon is 8. The measure of each side is 10 cm. So, the perimeter of the regular polygon is:
[tex]\text{Perimeter}=\text{Number of sides}\times\text{Measure of each side}[/tex]
[tex]\text{Perimeter}=8\times 10[/tex]
[tex]\text{Perimeter}=80[/tex]
Therefore, the perimeter of the regular polygon is 80.
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