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MATH / In the arrow-shaped polygon shown below, the angles at vertices A, C, D, E, and F are right angles, BC=FG=5, CD=FE=20, DE=10, and AB=AG. Find the area of polygon ABCDEFG. [asy] uni…

Problem

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

problem

In the arrow-shaped polygon shown below, the angles at vertices AA, CC, DD, EE, and FF are right angles, BC=FG=5BC = FG = 5, CD=FE=20CD = FE = 20, DE=10DE = 10, and AB=AGAB = AG. Find the area of polygon ABCDEFGABCDEFG. [asy] unitsize(1.5 cm); pair A, B, C, D, E, F, G; A = (0,0); B = (1,1); C = (1,0.5); D = (2.5,0.5); E = (2.5,-0.5); F = (1,-0.5); G = (1,-1); draw(A--B--C--D--E--F--G--cycle); label("AA", A, W); label("BB", B, NE); label("CC", C, S); label("DD", D, NE); label("EE", E, SE); label("FF", F, N); label("GG", G, SE); label("55", (B + C)/2, dir(0)); label("2020", (C + D)/2, N); label("1010", (D + E)/2, dir(0)); label("2020", (E + F)/2, S); label("55", (F + G)/2, dir(0)); [/asy]
Plain-text mathematical notation (without MathML)
In the arrow-shaped polygon shown below, the angles at vertices A, C, D, E, and F are right angles, BC=FG=5, CD=FE=20, DE=10, and AB=AG.  Find the area of polygon ABCDEFG.

[asy]
unitsize(1.5 cm);

pair A, B, C, D, E, F, G;

A = (0,0);
B = (1,1);
C = (1,0.5);
D = (2.5,0.5);
E = (2.5,-0.5);
F = (1,-0.5);
G = (1,-1);

draw(A--B--C--D--E--F--G--cycle);

label("A", A, W);
label("B", B, NE);
label("C", C, S);
label("D", D, NE);
label("E", E, SE);
label("F", F, N);
label("G", G, SE);
label("5", (B + C)/2, dir(0));
label("20", (C + D)/2, N);
label("10", (D + E)/2, dir(0));
label("20", (E + F)/2, S);
label("5", (F + G)/2, dir(0));
[/asy]
Original LaTeX notation
In the arrow-shaped polygon shown below, the angles at vertices $A$, $C$, $D$, $E$, and $F$ are right angles, $BC = FG = 5$, $CD = FE = 20$, $DE = 10$, and $AB = AG$.  Find the area of polygon $ABCDEFG$.

[asy]
unitsize(1.5 cm);

pair A, B, C, D, E, F, G;

A = (0,0);
B = (1,1);
C = (1,0.5);
D = (2.5,0.5);
E = (2.5,-0.5);
F = (1,-0.5);
G = (1,-1);

draw(A--B--C--D--E--F--G--cycle);

label("$A$", A, W);
label("$B$", B, NE);
label("$C$", C, S);
label("$D$", D, NE);
label("$E$", E, SE);
label("$F$", F, N);
label("$G$", G, SE);
label("$5$", (B + C)/2, dir(0));
label("$20$", (C + D)/2, N);
label("$10$", (D + E)/2, dir(0));
label("$20$", (E + F)/2, S);
label("$5$", (F + G)/2, dir(0));
[/asy]

level

Level 3

type

Geometry

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Source and history

task_id
95551fd5-3d21-549e-b2a2-b5c860e02352
task_key
geometry--test--95551fd5-3d21-549e-b2a2-b5c860e02352
task_revision_id
1
config / split
geometry / test

Official source

initial import