Question

A region is bounded by semicircular arcs constructed on the side of a square whose sides measure 2/\pi, as shown. What is the perimeter of this region?

Answer 1

Answer:

4

Step-by-step explanation:

The perimeter of the region is equal to the sum of the perimeter of the four semicircular arc. Since the semicircular arcs have the same measure, therefore:

Perimeter of region = 4 × Perimeter of semicircular arc.

The side of the square = diameter of the semicircle = 2/π.

The radius of semicircle = diameter/2 = $\frac{2/\pi}{2} =\frac{1}{\pi}$

The perimeter of a semicircle = perimeter of a circle ÷ 2

$Perimeter\ of \ semicircle = \frac{perimeter\ of\ circle}{2}=\frac{2\pi r}{2}=\frac{2\pi (\frac{1}{\pi} )}{2} =1\\ Perimeter\ of\ region = 4*Perimeter\ of \ semicircle=4*1=4$