AMC10 2003 B
AMC10 2003 B · Q23
AMC10 2003 B · Q23. It mainly tests Triangles (properties), Area & perimeter.
A regular octagon ABCDEFGH has an area of one square unit. What is the area of the rectangle ABEF? [Diagram shows regular octagon labeled A B C D E F G H clockwise]
一个正八边形ABCDEFGH的面积为一平方单位。矩形ABEF的面积是多少？[图示为顺时针标记A B C D E F G H的正八边形]
(A)
1 − √2 / 2
1 − √2 / 2
(B)
√2 / 4
√2 / 4
(C)
√2 − 1
√2 − 1
(D)
1/2
1/2
(E)
1 + √2 / 4
1 + √2 / 4
Answer
Correct choice: (D)
正确答案：（D）
Solution
(D) Let $O$ be the intersection of the diagonals of $ABEF$. Since the octagon is regular, $\triangle AOB$ has area $1/8$. Since $O$ is the midpoint of $AE$, $\triangle OAB$ and $\triangle BOE$ have the same area. Thus $\triangle ABE$ has area $1/4$, so $ABEF$ has area $1/2$.
(D) 设 $O$ 为 $ABEF$ 的对角线交点。由于该八边形是正八边形，$\triangle AOB$ 的面积为 $1/8$。因为 $O$ 是 $AE$ 的中点，$\triangle OAB$ 与 $\triangle BOE$ 的面积相同。因此 $\triangle ABE$ 的面积为 $1/4$，所以 $ABEF$ 的面积为 $1/2$。
Topics
Related Questions
Practice full AMC exams on amcdrill.
Try full-length practice and diagnostics at www.amcdrill.com.