AMC8 2006

AMC8 2006 · Q5

AMC8 2006 · Q5. It mainly tests Pythagorean theorem, Area & perimeter.

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?

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

(A) 15 15

(B) 20 20

(D) 30 30

(E) 40 40

Answer

Correct choice: (D)

正确答案：（D）

Solution

(D) Divide the larger square into 8 congruent triangles, as shown, 4 of which make up the smaller square. The area of the smaller square is $\frac{4}{8}$ or $\frac{1}{2}$ of the area of the larger square, so the area of the smaller square is equal to 30.

（D）如图所示，将较大的正方形分成 8 个全等三角形，其中 4 个组成较小的正方形。较小正方形的面积是较大正方形面积的 $\frac{4}{8}$，即 $\frac{1}{2}$，因此较小正方形的面积等于 30。

Topics