Question

O is the center of the regular decagon below. Find its perimeter. Round to the nearest

tenth if necessary.
16

Answer 1

Explanation:

The perimeter of the given polygon rounded to the nearest tenth is; 24.7

What is the perimeter of the Polygon?

The given polygon as we can see has 10 sides.

Now, when we draw a line from the center to the next vertex to the left of the one currently having a line, we will see that the angle can be calculated as; 360/10 = 36° because sum of exterior angles of a polygon sums up to 360°.

Thus, the other two angles will be; (180 - 36)/2 = 72° each

Using sine rule, we can find the length of a side of the polygon as;

x/sin 36 = 4/sin 72

x = (4 * sin 36)/sin 72

x = 2.472

Thus, perimeter = 2.472 * 10 = 24.72 ≈ 24.7