Find the Volume!
Source:
July 30, 2005
geometry3D geometryprismpyramidgeometric transformationreflectionrotation
Problem Statement
The solid shown has a square base of side length . The upper edge is parallel to the base and has length . All other edges have length . Given that , what is the volume of the solid?
[asy]
import three;
size(170);
pathpen = black+linewidth(0.65);
pointpen = black;
currentprojection = perspective(30,-20,10);
real s = 6 * 2^.5;
triple A=(0,0,0),B=(s,0,0),C=(s,s,0),D=(0,s,0),E=(-s/2,s/2,6),F=(3*s/2,s/2,6);
draw(F--B--C--F--E--A--B);
draw(A--D--E, dashed);
draw(D--C, dashed);
label("", (s/2, s/2, 6), N);
label("", (s/2, 0, 0), SW);
[/asy]