AMC8 2012

AMC8 2012 · Q6

AMC8 2012 · Q6. It mainly tests Arithmetic misc, Area & perimeter.

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?

一张矩形照片放置在一个四周边框宽度为2英寸的相框中。照片的高度为8英寸，宽度为10英寸。边框的面积是多少平方英寸？

(A) 36 36

(B) 40 40

(D) 72 72

(E) 88 88

Answer

Correct choice: (E)

正确答案：（E）

Solution

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 $8 \times 10 = 80$ 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 $12 \times 14 = 168$ square inches. Subtracting the area of the photograph from the area of both the frame and photograph, we find the answer to be $168-80 = \boxed{\textbf{(E)}\ 88}$.

要找出边框的面积，需要从照片加边框的总面积中减去照片的面积。照片的面积是$8 \times 10 = 80$平方英寸。整个相框（包括照片）的高度是$8+2+2 = 12$英寸，宽度是$10+2+2 = 14$英寸。因此，整个图形的面积是$12 \times 14 = 168$平方英寸。从照片加边框的总面积中减去照片的面积，我们得到答案$168-80 = \boxed{\textbf{(E)}\ 88}$。

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