IKMC 2025 - Grades 11-12 - Self-study Question 28

Question 28

A regular octagon has side length 1 cm. Eight circular arcs of radius 1 cm, centred at its vertices, are drawn as shown. What is the perimeter of the central dark region?

Question illustration

$\pi\text{ cm}$
$2\pi/3\text{ cm}$
$8\pi/9\text{ cm}$
$4\pi/5\text{ cm}$
$3\pi/4\text{ cm}$