Question

This figure shows how to create a six-pointed star from twelve equilateral triangle tiles:

[asy]
size(7cm);
pair cis(real magni, real argu) { return (magni*cos(argu*pi/180),magni*sin(argu*pi/180)); }

for(int i=90;i<450;i+=60) {
pair c=cis(1.2,i);
path p=c-cis(1,i)--c-cis(1,i+120)--c-cis(1,i-120)--cycle;
fill(p,orange+white);
draw(p);
pair c=cis(2.4,i);
path p=c+cis(1,i)--c+cis(1,i+120)--c+cis(1,i-120)--cycle;
fill(p,orange+white);
draw(p);
};

label("$\longrightarrow$",(4,0));
pair x=(8,0);
real s=sqrt(3);
path p=x+cis(s,0)--x+cis(3,30)--x+cis(s,60)--x+cis(3,90)--x+cis(s,120)--x+cis(3,150)--x+cis(s,180)--x+cis(3,210)--x+cis(s,240)--x+cis(3,270)--x+cis(s,300)--x+cis(3,330)--cycle;
fill(p,orange+white);
draw(p);
[/asy]
If each of the original tiles has a perimeter of $10$ cm, what is the perimeter of the final star in cm?

Answer 1

40 cm

Explanation:

The perimeter of the final figure has 12 edges, each of which is 1/3 of the perimeter of an original tile. The final star has a perimeter of ...

(12)(10 cm)/3 = 40 cm