Explanation

Perimeter = πr + 2r

where:

π is a mathematical constant approximately equal to 3.14159

r is the radius of the semicircle

In this problem, we know the total perimeter is 20.6 cm. So we can set up the equation:

20.6 = πr + 2r

To solve for r, we can factor out r on the right side:

20.6 = r(π + 2)

Then, we can divide both sides by π + 2 to isolate r:

r = 20.6 / (π + 2)

Using a calculator to evaluate this expression, we get:

r ≈ 4.0 cm

Therefore, the approximate radius of the semicircle is 4 cm.