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MATH / A diagonal of a polyhedron is a line segment connecting two non-adjacent…

Problem

Answer published by the source. Consult the official source to check your work against its answer.

problem

A diagonal of a polyhedron is a line segment connecting two non-adjacent vertices. How many diagonals does a pentagonal prism have? [asy]
import three;
size(100);
defaultpen(linewidth(0.7));
currentprojection = orthographic(-0.2,-1,2/3);

void drawPentagon (real h)
{

path3 y;

y=(0,0,h)--(3,0,h)--(5,3,h)--(3,6,h)--(0,5,h)--cycle;

draw(surface(y),white,nolight);

draw(y);
}

void drawRectangle(triple a, triple b, real h)
{

path3 y;

y=a--b--b+(0,0,h)--a+(0,0,h)--cycle;

draw(surface(y),white,black,nolight);
}

drawRectangle((0,0,0),(0,5,0),4);
drawRectangle((0,0,0),(3,0,0),4);
drawRectangle((3,0,0),(5,3,0),4);
drawPentagon(4);

//import three; currentprojection = orthographic(25,150,100); //defaultpen(linewidth(0.8)); size(100);
//void nGon(int numSides, real height){
//real angle = 360/numSides;
//for(int i = 0; i < numSides; ++i){
//draw(dir(angle*i,0)--dir(angle*(i + 1),0));
//draw((dir(angle*i,0) + (0,0,height))--(dir(angle*(i + 1),0) + (0,0,height)));
//draw(dir(angle*i,0)--(dir(angle*i,0) + (0,0,height)));
// }
//}
//nGon(5,2);
[/asy]

level

Level 5

type

Counting & Probability

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Source and history

task_id
429637ad-e5ec-549c-a05b-a4d38f91cbd4
task_key
counting~5fand~5fprobability--test--429637ad-e5ec-549c-a05b-a4d38f91cbd4
task_revision_id
1
config / split
counting_and_probability / test

Official source

initial import