Question

O is the center if the regular polygon beloe. Find its perimeter. Round to the nearest tenth if necessary HURRY

Answer 1

Answer:

24.8 units

Step-by-step explanation:

Given

$n = 10$ --- sides

The attached decagon

Required

The perimeter

The decagon is made up of 10 isosceles triangles.

The angle at the vertex of each is:

$Angle = \frac{360}{10}$

$Angle = 36$

Next, we create a right-angled triangle from the shape (see attachment)

$\theta$ is calculated as:

$\theta = \frac{Angle}{2}$

$\theta = \frac{36}{2}$

$\theta = 18$

Next, calculate x using:

$\sin(\theta) = \frac{Opposite}{Hypotenuse}$

So, we have:

$\sin(18) = \frac{x}{4}$

Make x the subject

$x = 4 * \sin(18)$

$x = 1.24$

So, the length (L) of one side of the decagon is:

$L = 2x$

$L = 2 * 1.24$

$L = 2.48$

The perimeter (P) of the shape is:

$P = 10 *L$

$P = 10 * 2.48$

$P = 24.8$

Answer 2

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

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