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Area of Quadrilateral in Rectangle

Source: 2012 AMC10B Problem #19

February 23, 2012

geometryrectangleAMCAMC 10AMC 10 Banalytic geometrysimilar triangles

Problem Statement

In rectangle

ABCD

,

AB=6

,

AD=30

, and

G

is the midpoint of

\overline{AD}

. Segment

AB

is extended

2

units beyond

B

to point

E

, and

F

is the intersection of

\overline{ED}

and

\overline{BC}

. What is the area of

BFDG

?

<span class='latex-bold'>(A)</span>\ \frac{133}{2}\qquad<span class='latex-bold'>(B)</span>\ 67\qquad<span class='latex-bold'>(C)</span>\ \frac{135}{2}\qquad<span class='latex-bold'>(D)</span>\ 68\qquad<span class='latex-bold'>(E)</span>\ \frac{137}{2}

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