AMC 8 2011 Problem 13

AMC8 2011 年第 13 题

面积与周长（综合）★★★☆☆

Two congruent squares, ABCD and PQRS , have side length 15 . They overlap to form the 15 by 25 rectangle AQRD shown. What percent of the area of rectangle AQRD is shaded?

ABCD 和 PQRS 是两个全等的正方形，边长均为 15.它们重合形成一个 15ｘ25 的矩形 AQRD，如图所示。那么阴影部分占了矩形 AQRD 面积的百分之多少？

A.15
B.18
C.20
D.24
E.25

正确答案 · Correct Answer

解析 · Solution

Solution 1

The length of BP is 5. the ratio of the areas is

\dfrac{5\cdot 15}{25\cdot 15}=\dfrac{5}{25}=20\%

-Megacleverstarfish15 To find the overlap length, we do the total length of the squares and subtract 25 (side length of figure). (15 + 15) - 25 = 5, so the overlap length is 5. To find what percentage of

AQRD

is shaded, we divide the shaded part by the area of the

AQRD

, so the percentage is

\dfrac{15 \cdot 5}{15 \cdot 25}

\dfrac{5}{25}

\dfrac{1}{5}

\dfrac{20}{100}

= 20 %, so the answer is

\textbf{(C)\ \text{20} }

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