MathDB

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 = \tfrac12 AB

. 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]

<span class='latex-bold'>(A) </span>\dfrac35\qquad<span class='latex-bold'>(B) </span>\dfrac57\qquad<span class='latex-bold'>(C) </span>\dfrac34\qquad<span class='latex-bold'>(D) </span>\dfrac79\qquad<span class='latex-bold'>(E) </span>\dfrac45

Problem Statement