MathDB

Equilateral

\triangle ABC

has side length

2

M

is the midpoint of

\overline{AC}

, and

C

is the midpoint of

\overline{BD}

. What is the area of

\triangle CDM

? [asy]size(200);defaultpen(linewidth(.8pt)+fontsize(8pt));
pair B = (0,0); pair A = 2*dir(60); pair C = (2,0); pair D = (4,0); pair M = midpoint(A--C);
label("

A

",A,NW);label("

B

",B,SW);label("

C

",C, SE);label("

M

",M,NE);label("

D

",D,SE);
draw(A--B--C--cycle); draw(C--D--M--cycle);[/asy]

<span class='latex-bold'>(A)</span>\ \frac {\sqrt {2}}{2}\qquad <span class='latex-bold'>(B)</span>\ \frac {3}{4}\qquad <span class='latex-bold'>(C)</span>\ \frac {\sqrt {3}}{2}\qquad <span class='latex-bold'>(D)</span>\ 1\qquad <span class='latex-bold'>(E)</span>\ \sqrt {2}

Problem Statement