AMC 8 1992 Problem 10

AMC8 1992 年第 10 题

三角形★★☆☆☆

An isosceles right triangle with legs of length 8 is partitioned into 16 congruent triangles as shown. The shaded area is

一个直角边长为 8 的等腰直角三角形被分成 16 个全等三角形，如图所示。着色面积是

正确答案 · Correct Answer

解析 · Solution

Solution 1

Because the smaller triangles are congruent, the shaded area take

\displaystyle \frac{10}{16}

of the largest triangles area, which is

\displaystyle \frac{8×8}{2} = 32

, so the shaded area is

\displaystyle \frac{10}{16} \times 32 = \text{(B) 20}

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