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MATH / ABCDEFGH shown below is a right rectangular prism. If the volume of pyramid ABCH is 20, then what is the volume of ABCDEFGH? [asy] import three; triple A,B,C,D,EE,F,G,H; A = (0,0,0…

Problem

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problem

ABCDEFGHABCDEFGH shown below is a right rectangular prism. If the volume of pyramid ABCHABCH is 20, then what is the volume of ABCDEFGHABCDEFGH? [asy] import three; triple A,B,C,D,EE,F,G,H; A = (0,0,0); B = (5,0,0); C = (5,6,0); D= (0,6,0); EE = (0,0,4); F = B+EE; G = C + EE; H = D + EE; draw(B--C--D); draw(B--A--D,dashed); draw(EE--F--G--H--EE); draw(A--EE,dashed); draw(B--F); draw(C--G); draw(D--H); label("AA",A,S); label("BB",B,W); label("CC",C,S); label("DD",D,E); label("EE",EE,N); label("FF",F,W); label("GG",G,SW); label("HH",H,E); [/asy]
Plain-text mathematical notation (without MathML)
ABCDEFGH shown below is a right rectangular prism.  If the volume of pyramid ABCH is 20, then what is the volume of ABCDEFGH?

[asy]

import three;

triple A,B,C,D,EE,F,G,H;

A = (0,0,0);

B = (5,0,0);

C = (5,6,0);

D= (0,6,0);

EE = (0,0,4);

F = B+EE;

G = C + EE;

H = D + EE;

draw(B--C--D);

draw(B--A--D,dashed);

draw(EE--F--G--H--EE);

draw(A--EE,dashed);

draw(B--F);

draw(C--G);

draw(D--H);

label("A",A,S);

label("B",B,W);

label("C",C,S);

label("D",D,E);

label("E",EE,N);

label("F",F,W);

label("G",G,SW);

label("H",H,E);

[/asy]
Original LaTeX notation
$ABCDEFGH$ shown below is a right rectangular prism.  If the volume of pyramid $ABCH$ is 20, then what is the volume of $ABCDEFGH$?

[asy]

import three;

triple A,B,C,D,EE,F,G,H;

A = (0,0,0);

B = (5,0,0);

C = (5,6,0);

D= (0,6,0);

EE = (0,0,4);

F = B+EE;

G = C + EE;

H = D + EE;

draw(B--C--D);

draw(B--A--D,dashed);

draw(EE--F--G--H--EE);

draw(A--EE,dashed);

draw(B--F);

draw(C--G);

draw(D--H);

label("$A$",A,S);

label("$B$",B,W);

label("$C$",C,S);

label("$D$",D,E);

label("$E$",EE,N);

label("$F$",F,W);

label("$G$",G,SW);

label("$H$",H,E);

[/asy]

level

Level 5

type

Geometry

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Source and history

task_id
d396479e-7951-550d-bfc3-58d6fb0a51dc
task_key
geometry--test--d396479e-7951-550d-bfc3-58d6fb0a51dc
task_revision_id
1
config / split
geometry / test

Official source

initial import