Problem #2344


What is the area of the shaded region of the given $8\times 5$ rectangle?

[asy]  size(6cm); defaultpen(fontsize(9pt)); draw((0,0)--(8,0)--(8,5)--(0,5)--cycle); filldraw((7,0)--(8,0)--(8,1)--(0,4)--(0,5)--(1,5)--cycle,gray(0.8));  label("$1$",(1/2,5),dir(90)); label("$7$",(9/2,5),dir(90));  label("$1$",(8,1/2),dir(0)); label("$4$",(8,3),dir(0));  label("$1$",(15/2,0),dir(270)); label("$7$",(7/2,0),dir(270));  label("$1$",(0,9/2),dir(180)); label("$4$",(0,2),dir(180));  [/asy]

$\textbf{(A)}\ 4\dfrac{3}{4}\qquad\textbf{(B)}\ 5\qquad\textbf{(C)}\ 5\dfrac{1}{4}\qquad\textbf{(D)}\ 6\dfrac{1}{2}\qquad\textbf{(E)}\ 8$

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Instructions for entering answers:

  • Reduce fractions to lowest terms and enter in the form 7/9.
  • Numbers involving pi should be written as 7pi or 7pi/3 as appropriate.
  • Square roots should be written as sqrt(3), 5sqrt(5), sqrt(3)/2, or 7sqrt(2)/3 as appropriate.
  • Exponents should be entered in the form 10^10.
  • If the problem is multiple choice, enter the appropriate (capital) letter.
  • Enter points with parentheses, like so: (4,5)
  • Complex numbers should be entered in rectangular form unless otherwise specified, like so: 3+4i. If there is no real component, enter only the imaginary component (i.e. 2i, NOT 0+2i).

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