Problem

2017 AMC 10A Problem 3

Tamara has three rows of two 6-feet by 2-feet flower beds in her garden. The beds are separated and also surrounded by 1-foot-wide walkways, as shown on the diagram. What is the total area of the walkways, in square feet?

[asy] draw((0,0)--(0,10)--(15,10)--(15,0)--cycle); fill((0,0)--(0,10)--(15,10)--(15,0)--cycle, lightgray); draw((1,1)--(1,3)--(7,3)--(7,1)--cycle); fill((1,1)--(1,3)--(7,3)--(7,1)--cycle, white); draw((1,4)--(1,6)--(7,6)--(7,4)--cycle); fill((1,4)--(1,6)--(7,6)--(7,4)--cycle, white); draw((1,7)--(1,9)--(7,9)--(7,7)--cycle); fill((1,7)--(1,9)--(7,9)--(7,7)--cycle, white); draw((8,1)--(8,3)--(14,3)--(14,1)--cycle); fill((8,1)--(8,3)--(14,3)--(14,1)--cycle, white); draw((8,4)--(8,6)--(14,6)--(14,4)--cycle); fill((8,4)--(8,6)--(14,6)--(14,4)--cycle, white); draw((8,7)--(8,9)--(14,9)--(14,7)--cycle); fill((8,7)--(8,9)--(14,9)--(14,7)--cycle, white); defaultpen(fontsize(8, lineskip=1)); label("2", (1.2, 2)); label("6", (4, 1.2)); defaultpen(linewidth(.2)); draw((0,8)--(1,8), arrow=Arrows); draw((7,8)--(8,8), arrow=Arrows); draw((14,8)--(15,8), arrow=Arrows); draw((11,0)--(11,1), arrow=Arrows); draw((11,3)--(11,4), arrow=Arrows); draw((11,6)--(11,7), arrow=Arrows); label("1", (.5,7.8)); label("1", (7.5,7.8)); label("1", (14.5,7.8)); label("1", (10.8,.5)); label("1", (10.8,3.5)); label("1", (10.8,6.5)); [/asy]


\textbf{(A)}\ 72\qquad\textbf{(B)}\ 78\qquad\textbf{(C)}\ 90\qquad\textbf{(D)}\ 120\qquad\textbf{(E)}\ 150


Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.


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