2018 AMC 10B Problems/Problem 10
Revision as of 14:30, 16 February 2018 by Ishankhare (talk | contribs) (Created page with "In the rectangular parallelpiped shown, <math>AB</math> = 3, <math>BC</math> = 1, and <math>CG</math> = 2. Point <math>M</math> is the midpoint of <math>\overline{FG}</math>....")
In the rectangular parallelpiped shown, 
= 3, 
= 1, and 
= 2. Point 
is the midpoint of 
. What is the volume of the rectangular pyramid with base 
and apex ?
[asy]
size(250);
defaultpen(fontsize(10pt));
pair A =origin;
pair B = (4.75,0);
pair E1=(0,3);
pair F = (4.75,3);
pair G = (5.95,4.2);
pair C = (5.95,1.2);
pair D = (1.2,1.2);
pair H= (1.2,4.2);
pair M = ((4.75+5.95)/2,3.6);
draw(E1--M--H--E1--A--B--E1--F--B--M--C--G--H);
draw(B--C);
draw(F--G);
draw(A--D--H--C--D,dashed);
label("
",A,SW);
label("
",B,SE);
label("
",C,E);
label("
",D,W);
label("
",E1,W);
label("
",F,SW);
label("
",G,NE);
label("
",H,NW);
label("",M,N);
dot(A);
dot(B);
dot(E1);
dot(F);
dot(G);
dot(C);
dot(D);
dot(H);
dot(M);[/asy]
