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Geometry Difficulty 2.7 Junior Find the answer Canada

The line passing through the points $A$ , $B$ , $C$ , and $D$ , is parallel to the line passing
through the points $E$ , $F$ , and $G$ , as shown.

$ABFE$ is a parallelogram and
$CDG$ is a triangle. If $AB = 8~\text{cm}$ and $CD = 12~\text{cm}$ , what is the ratio of
the area of $ABFE$ to the area of
$\triangle CDG$ ?

Pick one

Solution

The distance between two parallel lines is constant. Thus, the
height of parallelogram $ABFE$ is
equal to the height of $\$\triangle$
CDG$.

Suppose that height is $h$ . In this
case, the ratio of the area of $ABFE$
to the area of $\triangle CDG$ is
$\$AB\times h:\dfrac12\times CD\times$
h$.

Substituting and simplifying, this ratio is equal to $\$8\times h:\dfrac12\times12\times$
h=8:6=4:3$.

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Source: CEMC, University of Waterloo, licensed CC-BY-NC-4.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project.