AMC 8 2001 Problem 11

AMC8 2001 年第 11 题

坐标几何★★★☆☆

Points

A

B

C

and

D

have these coordinates:

A(3,2)

B(3,-2)

C(-3,-2)

and

D(-3, 0)

. The area of quadrilateral

ABCD

点

A

，

B

，

C

和

D

有如下坐标：

A(3,2)

，

B(3,-2)

，

C(-3,-2)

，

D(-3,0)

，则四边形

ABCD

的面积为

A.12
B.15
C.18
D.21
E.24

正确答案 · Correct Answer

解析 · Solution

Solution 1

Using the diagram above, the figure can be divided along the x-axis into two familiar regions that do not overlap: a right triangle and a rectangle. Since the areas do not overlap, the area of the entire trapezoid is the sum of the area of the triangle and the area of the rectangle.

A_{trap} = A_{tri} + A_{rect}

\displaystyle A_{trap} = \frac{1}{2} bh + lw

\displaystyle A_{trap} = \frac{1}{2} \cdot 6 \cdot 2 + 6\cdot 2

A_{trap} = 6 + 12 = 18 \rightarrow C

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