Question

点 $A, B, C$ 和 $D$ 是大正方形各边的中点。如果大正方形面积为 $60$ ，小正方形的面积是多少？

Points $A, B, C$ and $D$ are midpoints of the sides of the larger square. If the larger square has area $60,$ what is the area of the smaller square?

$15$

$20$

$24$

$30$

$40$

答案：D

知识点：正方形（几何）中点面积分割

难度评级：820

解答：

可以把所有三角形向内折叠，正好覆盖小正方形。这说明小正方形的面积是大正方形面积的一半。

所以小正方形面积为 $60 \div 2 = 30$ 。

所以正确答案是 D。

Note that we can fold all the triangles in to perfectly cover the smaller square. This means that area of the smaller square is half the area of the larger square.

This makes the area of the smaller square $60 \div 2 = 30.$

Thus, D is the correct answer.

2006 AMC 8 第 5 题

答案：D

难度评级：820

解答：

其他年份的第 5 题