1 Answer

Bryan Butler · Answer 1 · 2022-06-02T09:00:32+0000

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:

$S=(n-2)180^\circ$

Sum of all the interior angles of a regular polygon is 1080°.

$1080^\circ=(n-2)180^\circ$

$(1080^\circ)/(180^\circ)=n-2$

6+2=n

8=n

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:

$\text{Perimeter}=\text{Number of sides}*\text{Measure of each side}$

$\text{Perimeter}=8* 10$

$\text{Perimeter}=80$

Therefore, the perimeter of the regular polygon is 80.

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