Three circles each having radius equal to 4 cm, are drawn with the vertices of an equilateral triangle as the centers.  If the length of each side of the triangle is equal to 12 cm, then what is the area (in cm²) of the portion of the triangle that is not covered by the sectors of the circles?

18 (2\(\sqrt {3}\) - \(\pi \))

Area of three sectors =area of one circle (because sum of angle of all three sectors = 180°)

Area of shaded portion = Area of equilateral triangle - \(\frac{1}{2}\) Area of circle

= \(\frac{\sqrt {3}}{4}\) (12)² - \(\frac{1}{2}\)\(\pi \) (6)²

= \(\sqrt {3}\) × 6 × 6 - \(\pi \) × 6 × 3

= 6 (6\(\sqrt {3}\) - 3\(\pi \)) = 18 (2\(\sqrt {3}\) - \(\pi \))