jmc

Question

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

Accepted Answer

Because the figure has rotational symmetry,

Q

is the midpoint of

Z W

. Consequently, the triangles

B Z Q

and

B W Q

have the same area because they share a height and have bases that are the same length. We have

[B Q W] = \frac{1}{2} [B Z W] = \frac{1}{2} ([A B W Z] - [A B Z])

= \frac{1}{2} (120 - \frac{1}{2} \cdot 6 \cdot 12) = \frac{1}{2} (120 - 36) = \frac{84}{2} = 42 .