AMC12 2002 A

AMC12 2002 A · Q8

AMC12 2002 A · Q8. It mainly tests Area & perimeter.

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 $P$ the area of the red square. Which of the following is correct?

Betsy 用蓝色三角形、小白色正方形和一个红色中心正方形设计了一面旗帜，如图所示。设 $B$ 为蓝色三角形的总面积，$W$ 为白色正方形的总面积，$P$ 为红色正方形的面积。以下哪项正确？

(A) B = W B = W

(B) W = R W = R

(D) 3B = 2R 3B = 2R

(E) 2R = W 2R = W

Answer

Correct choice: (A)

正确答案：（A）

Solution

The blue that's touching the center red square makes up 8 triangles, or 4 squares. Each of the corners is 1 square and each of the edges is 1, totaling 12 squares. There are 12 white squares, thus we have $\boxed{B=W\Rightarrow \text{(A)}}$.

与中心红色正方形相接触的蓝色部分由 8 个三角形组成，也就是 4 个正方形。四个角各是 1 个正方形，每条边各是 1 个正方形，总计 12 个正方形。白色正方形共有 12 个，因此 $\boxed{B=W\Rightarrow \text{(A)}}$。

Topics

GE.007 Area & perimeter