AMC 8 2012 Problem 6

AMC8 2012 年第 6 题

四边形与多边形★☆☆☆☆

A rectangular photograph is placed in a frame that forms a border two inches wide on all sides of the photograph. The photograph measures 8 inches high and 10 inches wide. What is the area of the border, in square inches?

一张长方形的照片被放置在一个框架中，框架在照片的四周形成一个两英寸宽的边界。这张照片高 8 英寸，宽 10 英寸。边界的面积是多少平方英寸？

A. $\hspace{.05in}36$
B. $\hspace{.05in}40$
C. $\hspace{.05in}64$
D. $\hspace{.05in}72$
E. $\hspace{.05in}88$

正确答案 · Correct Answer

解析 · Solution

Solution 1

In order to find the area of the frame, we need to subtract the area of the photograph from the area of the photograph and the frame together. The area of the photograph is 8×10 = 80 square inches. The height of the whole frame (including the photograph) would be 8+2+2 = 12, and the width of the whole frame, 10+2+2 = 14. Therefore, the area of the whole figure would be 12×14 = 168 square inches. Subtracting the area of the photograph from the area of both the frame and photograph, we find the answer to be 168-80 = 88.

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