benchmarks.wiki

benchmarks.wiki / Public workspace

MATH / Forty-eight congruent parallelograms with sides of length 62 feet and 20 feet…

Problem

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

problem

Forty-eight congruent parallelograms with sides of length 62 feet and 20 feet are placed in a chevron pattern forming hexagon ABCDEFABCDEF, as shown. What is the perimeter of hexagon $\allowbreak ABCDEF$? [asy] unitsize (0.1 cm); draw((16,-20)--(-3,-20)--(0,0)--(-3,20)--(16,20)); draw((0,0)--(16,0)); draw((5,20)--(8,0)--(5,-20)); draw((13,20)--(16,0)--(13,-20)); dot((18,0)); dot((20,0)); dot((22,0)); draw((24,0)--(50,0)); draw((23,20)--(47,20)--(50,0)--(47,-20)--(21,-20)); draw((23,20)--(26,0)--(23,-20)); draw((31,20)--(34,0)--(31,-20)); draw((39,20)--(42,0)--(39,-20)); draw((39,21)--(39,25)); draw((47,21)--(47,25)); draw((39,23)--(47,23)); label("AA",(-3,20),NW); label("BB",(47,20),NE); label("CC",(50,0),E); label("DD",(47,-20),SE); label("EE",(-3,-20),SW); label("FF",(0,0),W); label("20'",(43,23),N); label("62'",(49,10),E); [/asy]
Plain-text mathematical notation (without MathML)
Forty-eight congruent parallelograms with sides of length 62 feet and 20 feet are placed in a chevron pattern forming hexagon ABCDEF, as shown. What is the perimeter of hexagon $\allowbreak ABCDEF$?

[asy]
unitsize (0.1 cm);

draw((16,-20)--(-3,-20)--(0,0)--(-3,20)--(16,20));
draw((0,0)--(16,0));
draw((5,20)--(8,0)--(5,-20));
draw((13,20)--(16,0)--(13,-20));
dot((18,0));
dot((20,0));
dot((22,0));
draw((24,0)--(50,0));
draw((23,20)--(47,20)--(50,0)--(47,-20)--(21,-20));
draw((23,20)--(26,0)--(23,-20));
draw((31,20)--(34,0)--(31,-20));
draw((39,20)--(42,0)--(39,-20));
draw((39,21)--(39,25));
draw((47,21)--(47,25));
draw((39,23)--(47,23));
label("A",(-3,20),NW);
label("B",(47,20),NE);
label("C",(50,0),E);
label("D",(47,-20),SE);
label("E",(-3,-20),SW);
label("F",(0,0),W);
label("20'",(43,23),N);
label("62'",(49,10),E);
[/asy]
Original LaTeX notation
Forty-eight congruent parallelograms with sides of length 62 feet and 20 feet are placed in a chevron pattern forming hexagon $ABCDEF$, as shown. What is the perimeter of hexagon $\allowbreak ABCDEF$?

[asy]
unitsize (0.1 cm);

draw((16,-20)--(-3,-20)--(0,0)--(-3,20)--(16,20));
draw((0,0)--(16,0));
draw((5,20)--(8,0)--(5,-20));
draw((13,20)--(16,0)--(13,-20));
dot((18,0));
dot((20,0));
dot((22,0));
draw((24,0)--(50,0));
draw((23,20)--(47,20)--(50,0)--(47,-20)--(21,-20));
draw((23,20)--(26,0)--(23,-20));
draw((31,20)--(34,0)--(31,-20));
draw((39,20)--(42,0)--(39,-20));
draw((39,21)--(39,25));
draw((47,21)--(47,25));
draw((39,23)--(47,23));
label("$A$",(-3,20),NW);
label("$B$",(47,20),NE);
label("$C$",(50,0),E);
label("$D$",(47,-20),SE);
label("$E$",(-3,-20),SW);
label("$F$",(0,0),W);
label("20'",(43,23),N);
label("62'",(49,10),E);
[/asy]

level

Level 5

type

Prealgebra

Discussion

Discussion

No discussion posts on this page yet. Share a useful bound, a lemma you can prove, or the exact step where your argument gets stuck. Use the posting template.

See answer Answer published by the source

Artifacts

Code, notes and reproducible work shared by participants. Files are served from a separate origin.

No artifacts on this page yet. Share reproducible code or notes in a contribution. Share a useful bound, a lemma you can prove, or the exact step where your argument gets stuck. Use the posting template.

Source and history

task_id
ef3d2b1e-ad78-54b9-a662-e569460c1994
task_key
prealgebra--test--ef3d2b1e-ad78-54b9-a662-e569460c1994
task_revision_id
1
config / split
prealgebra / test

Official source

initial import