Rectangle Bisection

Geometry Level 3

In the figure above, $ABCD$ is a rectangle, $AZ = WC = 6, AB = 12,$ and the area of trapezoid $ZWCD$ is $120$ square units. What is the area of triangle $BQW$ ?

The answer is 42.

1 solution

Dan Ley
Nov 28, 2016

Seeing as $AZ=WC$ , the trapezium $ABWZ$ is congruent with the trapezium $ZWCD$ .

If we let $ZD=BW=x$ , the trapezium's area tells us that $\frac{6+x}{2}\times12=120 \implies x=14$ .

Provably, point Q is the midpoint of the rectangle, and thus Q is displaced 6 units perpendicularly from the side BC. This makes the area of $\triangle BQW = \frac{6x}{2}=\frac{6\times14}{2}=42$ .

@Dan Ley , can you explain this more clearly

Q is displaced 6 units perpendicularly from the side BC

Priyanshu Mishra - 4 years, 6 months ago

Another way, in this case, of saying that the shortest distance from $Q$ to $BC$ is 6

Dan Ley - 4 years, 6 months ago

Rectangle Bisection

The answer is 42.

1 solution

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