Step 1:

Hypo cycloid perimeter: .

Arc length of the curve:

If a curve is described by parametric equations and , where are continuous on, then the arc length of the curve is, .

Consider .

Find  .

Find .

Substitute and values in the arc length formula.

Periodicity of is .

In the interval , we can write integral as four multiples of single integral considering in

In the interval  ,

Using limit properties of integration, we can write the integral as

Solution:

Arc length of the curve is .