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MATH / If a, b, and c are consecutive integers, find the area of the shaded region in the square below: [asy] size(1.75inch); pair A, B, C, D, W, X, Y, Z; A = (0,0); B = (7,0); C = (7,7);…

Problem

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

problem

If aa, bb, and cc are consecutive integers, find the area of the shaded region in the square below: [asy] size(1.75inch); pair A, B, C, D, W, X, Y, Z; A = (0,0); B = (7,0); C = (7,7); D = (0,7); W = (3,0); X = (7,3); Y = (4,7); Z = (0,4); draw(A--B--C--D--cycle); draw(W--X--Y--Z--cycle); fill(A--W--Z--cycle, gray); fill(B--X--W--cycle, gray); fill(C--Y--X--cycle, gray); fill(D--Z--Y--cycle, gray); label("aa", A--W); label("bb", W--B); label("aa", B--X); label("bb", X--C); label("aa", C--Y); label("bb", Y--D); label("aa", D--Z); label("bb", Z--A); label("cc", W--X, NW); label("cc", X--Y, SW); label("cc", Y--Z, SE); label("cc", Z--W, NE); [/asy]
Plain-text mathematical notation (without MathML)
If a, b, and c are consecutive integers, find the area of the shaded region in the square below: [asy]
size(1.75inch);
pair A, B, C, D, W, X, Y, Z;
A = (0,0); B = (7,0); C = (7,7); D = (0,7);
W = (3,0); X = (7,3); Y = (4,7); Z = (0,4);
draw(A--B--C--D--cycle); draw(W--X--Y--Z--cycle);
fill(A--W--Z--cycle, gray); fill(B--X--W--cycle, gray); fill(C--Y--X--cycle, gray); fill(D--Z--Y--cycle, gray);
label("a", A--W); label("b", W--B); label("a", B--X); label("b", X--C);
label("a", C--Y); label("b", Y--D); label("a", D--Z); label("b", Z--A);
label("c", W--X, NW); label("c", X--Y, SW); label("c", Y--Z, SE); label("c", Z--W, NE);
[/asy]
Original LaTeX notation
If $a$, $b$, and $c$ are consecutive integers, find the area of the shaded region in the square below: [asy]
size(1.75inch);
pair A, B, C, D, W, X, Y, Z;
A = (0,0); B = (7,0); C = (7,7); D = (0,7);
W = (3,0); X = (7,3); Y = (4,7); Z = (0,4);
draw(A--B--C--D--cycle); draw(W--X--Y--Z--cycle);
fill(A--W--Z--cycle, gray); fill(B--X--W--cycle, gray); fill(C--Y--X--cycle, gray); fill(D--Z--Y--cycle, gray);
label("$a$", A--W); label("$b$", W--B); label("$a$", B--X); label("$b$", X--C);
label("$a$", C--Y); label("$b$", Y--D); label("$a$", D--Z); label("$b$", Z--A);
label("$c$", W--X, NW); label("$c$", X--Y, SW); label("$c$", Y--Z, SE); label("$c$", Z--W, NE);
[/asy]

level

Level 3

type

Geometry

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Source and history

task_id
36998ee6-fcbd-557d-ab58-36a0370af776
task_key
geometry--test--36998ee6-fcbd-557d-ab58-36a0370af776
task_revision_id
1
config / split
geometry / test

Official source

initial import