AMC8 1993

AMC8 1993 · Q18

AMC8 1993 · Q18. It mainly tests Area & perimeter, Coordinate geometry.

The rectangle shown has length AC = 32, width AE = 20, and B and F are midpoints of AC and AE, respectively. The area of the quadrilateral ABDF is

如图所示的矩形，长AC=32，宽AE=20，B和F分别是AC和AE的中点。四边形ABDF的面积是

(A) 320 320

(B) 325 325

(D) 335 335

(E) 340 340

Answer

Correct choice: (A)

正确答案：（A）

Solution

Answer (A): Rectangle $ACDE$ has area $32 \times 200 = 640$. Triangle $BCD$ has area $(16 \times 20)/2 = 160$, and triangle $DEF$ has area $(10 \times 32)/2 = 160$. The remaining area, $ABDF$, is $640 - (160 + 160) = 320$.

答案（A）：矩形 $ACDE$ 的面积为 $32 \times 200 = 640$。三角形 $BCD$ 的面积为 $(16 \times 20)/2 = 160$，三角形 $DEF$ 的面积为 $(10 \times 32)/2 = 160$。剩余部分 $ABDF$ 的面积为 $640 - (160 + 160) = 320$。

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