Question

Betsy 用蓝色三角形、小白色正方形和红色中心正方形设计了一面旗帜，如图所示。设 $B$ 为蓝色三角形总面积， $W$ 为白色正方形总面积， $R$ 为红色正方形面积。下列哪一项正确？

Betsy designed a flag using blue triangles, small white squares, and a red center square, as shown. Let $B$ be the total area of the blue triangles, $W$ the total area of the white squares, and $R$ the area of the red square. Which of the following is correct?

$B = W$

$W = R$

$B = R$

$3B = 2R$

$2R = W$

答案：A

知识点：面积分割全等（几何）

难度评级：1380

解答：

画出所示的对角线后，整面旗帜被分成全等三角形。数一数可得，蓝色区域有 $24$ 个三角形，白色区域有 $24$ 个，红色正方形有 $16$ 个。

由于蓝色和白色区域含有相同数量的三角形，所以 $B = W$ 。

因此，正确答案是 A。

Drawing the diagonals shown, the entire flag is tiled by congruent triangles. Counting, there are $24$ triangles in the blue region, $24$ in the white region, and $16$ in the red square.

Since the blue and white regions contain the same number of triangles, $B = W.$

Thus, the correct answer is A.

2002 AMC 12A 第 8 题

答案：A

难度评级：1380

解答：

其他年份的第 8 题