AMC8 1994

AMC8 1994 · Q12

AMC8 1994 · Q12. It mainly tests Area & perimeter, Geometry misc.

Each of the three large squares shown below is the same size. Segments that intersect the sides of the squares intersect at the midpoints of the sides. How do the shaded areas of these squares compare?

下面的三个大正方形大小相同。穿过正方形边的线段都在边的中点相交。这些正方形的阴影面积如何比较？

(A) The shaded area in all three are equal. 三个阴影面积相等。

(B) Only the shaded areas of I and II are equal. 仅I和II阴影面积相等。

(D) Only the shaded areas of II and III are equal. 仅II和III阴影面积相等。

(E) The shaded areas of I, II and III are all different. I、II、III阴影面积均不同。

Answer

Correct choice: (A)

正确答案：（A）

Solution

The shaded area of square II is 1/4 of the total. In I, two triangles each 1/8 total, sum 1/4. In III, four triangles each 1/16, sum 1/4. All equal.

正方形II的阴影面积是总面积的1/4。I中两个三角形各占总面积的1/8，相加为1/4。III中四个三角形各占1/16，相加为1/4。全都相等。

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