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MATH / In the diagram, D and E are the midpoints of (AB)¯ and (BC)¯ respectively. Determine the area of quadrilateral DBEF. [asy] size(180); defaultpen(linewidth(.7pt)+fontsize(10pt)); pa…

Problem

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

problem

In the diagram, DD and EE are the midpoints of AB¯\overline{AB} and BC¯\overline{BC} respectively. Determine the area of quadrilateral DBEFDBEF. [asy] size(180); defaultpen(linewidth(.7pt)+fontsize(10pt)); pair A, B, C, D, E, F; A=(0,6); B=(0,0); C=(8,0); D=(0,3); E=(4,0); F=(8/3,2); draw(E--A--C--D); draw((-1,0)--(10,0), EndArrow); draw((0,-1)--(0,8), EndArrow); label("A(0,6)A(0,6)", A, W); label("B(0,0)B(0,0)", B, SW); label("C(8,0)C(8,0)", C, S); label("DD", D, W); label("EE", E, S); label("FF", F, SW); label("xx", (10,0), dir(0)); label("yy", (0,8), dir(90)); [/asy]
Plain-text mathematical notation (without MathML)
In the diagram, D and E are the midpoints of (AB)¯ and (BC)¯ respectively.  Determine the area of quadrilateral DBEF. [asy]
size(180); defaultpen(linewidth(.7pt)+fontsize(10pt));
pair A, B, C, D, E, F;
A=(0,6);
B=(0,0);
C=(8,0);
D=(0,3);
E=(4,0);
F=(8/3,2);
draw(E--A--C--D);
draw((-1,0)--(10,0), EndArrow);
draw((0,-1)--(0,8), EndArrow);
label("A(0,6)", A, W);
label("B(0,0)", B, SW);
label("C(8,0)", C, S);
label("D", D, W);
label("E", E, S);
label("F", F, SW);
label("x", (10,0), dir(0));
label("y", (0,8), dir(90));
[/asy]
Original LaTeX notation
In the diagram, $D$ and $E$ are the midpoints of $\overline{AB}$ and $\overline{BC}$ respectively.  Determine the area of quadrilateral $DBEF$. [asy]
size(180); defaultpen(linewidth(.7pt)+fontsize(10pt));
pair A, B, C, D, E, F;
A=(0,6);
B=(0,0);
C=(8,0);
D=(0,3);
E=(4,0);
F=(8/3,2);
draw(E--A--C--D);
draw((-1,0)--(10,0), EndArrow);
draw((0,-1)--(0,8), EndArrow);
label("$A(0,6)$", A, W);
label("$B(0,0)$", B, SW);
label("$C(8,0)$", C, S);
label("$D$", D, W);
label("$E$", E, S);
label("$F$", F, SW);
label("$x$", (10,0), dir(0));
label("$y$", (0,8), dir(90));
[/asy]

level

Level 4

type

Geometry

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Source and history

task_id
85551fd5-0145-51fd-ad6c-1fdb9f68a9cc
task_key
geometry--test--85551fd5-0145-51fd-ad6c-1fdb9f68a9cc
task_revision_id
1
config / split
geometry / test

Official source

initial import