Problems(1)
Regular hexagon ABCDEF has area 1. Starting with edge AB and moving clockwise, a new point is drawn exactly one half of the way along each side of the hexagon. For example, on side AB, the new point, G, is drawn so AG=21AB. This forms hexagon GHIJKL, as shown. What is the area of this new hexagon?
[asy]
size(120);
pair A = (-1/2, sqrt(3)/2);
pair B = (1/2, sqrt(3)/2);
pair C = (1,0);
pair D = (1/2, -sqrt(3)/2);
pair EE = (-1/2, -sqrt(3)/2);
pair F = (-1,0);
pair G = (A+B)/2;
pair H = (B+C)/2;
pair I = (C+D)/2;
pair J = (D+EE)/2;
pair K = (EE+F)/2;
pair L = (F+A)/2;
draw(A--B--C--D--EE--F--cycle);
draw(G--H--I--J--K--L--cycle);
dot(A^^B^^C^^D^^EE^^F^^G^^H^^I^^J^^K^^L);
label("A",A,NW);
label("B",B,NE);
label("C",C,E);
label("D",D,SE);
label("E",EE,SW);
label("F",F,W);
label("G",G,N);
label("H",H,NE);
label("I",I,SE);
label("J",J,S);
label("K",K,SW);
label("L",L,NW);
[/asy]
<spanclass=′latex−bold′>(A)</span>53<spanclass=′latex−bold′>(B)</span>75<spanclass=′latex−bold′>(C)</span>43<spanclass=′latex−bold′>(D)</span>97<spanclass=′latex−bold′>(E)</span>54 2019 Individual