Question

点 $A$ 、 $B$ 、 $C$ 和 $D$ 的坐标分别为 $A(3,2)$ 、 $B(3,-2)$ 、 $C(-3,-2)$ 和 $D(-3,0)$ 。四边形 $ABCD$ 的面积是多少？

Points $A,$ $B,$ $C$ and $D$ have these coordinates: $A(3,2),$ $B(3,-2),$ $C(-3,-2)$ and $D(-3,0).$ What is the area of quadrilateral $ABCD?$

$12$

$15$

$18$

$21$

$24$

因为 $\overline{DC} \parallel \overline{AB}$ ，所以 $ABCD$ 是梯形。

梯形面积公式为 $A = \dfrac{1}{2} (b_1 + b_2) h.$

代入和可得 $b_1 = DC = 2,$ $b_2 = AB = 4,$ $h = CB = 6,$ $A = \dfrac{1}{2} (2 + 4) \cdot 6$ $= \dfrac{1}{2} \cdot 6 \cdot 6 = 18.$

所以正确答案是 C。

We can see that $ABCD$ is a trapezoid since $\overline{DC} \parallel \overline{AB}.$

Recall that the formula for the area of a trapezoid is $A = \dfrac{1}{2} (b_1 + b_2) h.$

Plugging in $b_1 = DC = 2,$ $b_2 = AB = 4,$ and $h = CB = 6,$ we get that $A = \dfrac{1}{2} (2 + 4) \cdot 6$ $= \dfrac{1}{2} \cdot 6 \cdot 6 = 18.$

Thus, C is the correct answer.