Btukfyl

I have a TikZ diagram to the right of a minipage environment. I have some text that I want under the minipage environment. The interline spacing is about half of the other interline spacing.

I don't insist on using a minipage here. I just want the appropriate typesetting.

documentclass{amsart}

usepackage{mathtools}



usepackage[dvipsnames]{xcolor}

usepackage{tikz}

usetikzlibrary{calc,intersections}



usepackage{pgfplots}

pgfplotsset{compat=1.11}



setlength{oddsidemargin}{0.0in}

setlength{evensidemargin}{0.0in} setlength{textwidth}{6.1in}

setlength{topmargin}{0.0in} setlength{textheight}{9in}





begin{document}







noindent begin{minipage}[t]{4.875in}

noindent raggedright{textbf{1.) }The following figure depicts three congruent semicircles bounded by another \

semicircle; the diameters of the three smaller semicircles cover the diameter of \

the bigger semicircle, and each of the three smaller semicircles is tangent to \

two other semicircles at the endpoints of its diameter. textit{A} is the area of \

of the region enclosed by the three smaller semicircles and textit{B} is the area}

end{minipage}

%

hspace{-0.25cm}

%

raisebox{0mm}[0mm][0mm]

{

begin{tikzpicture}[baseline=(current bounding box.north west)]



coordinate (O) at (0,0);

draw[fill=blue!50] (-1.5,0) -- (1.5,0) arc (0:180:1.5) -- cycle;

%

draw[fill=yellow] (-3/2,0) -- (-1/2,0) arc (0:180:1/2) -- cycle;

draw[fill=yellow] (-1/2,0) -- (1/2,0) arc (0:180:1/2) -- cycle;

draw[fill=yellow] (1/2,0) -- (3/2,0) arc (0:180:1/2) -- cycle;



draw[fill] (O) circle (1.5pt);





end{tikzpicture}

} \

the region enclosed by the big semicircle but outside the three smaller semicircles. Compute the ratio of $A : B$.





end{document}

You want to look at How to keep a constant baselineskip when using minipages (or parboxes)? but there's a much better alternative:

documentclass{amsart}

usepackage{mathtools}



usepackage{wrapfig}



usepackage[dvipsnames]{xcolor}

usepackage{tikz}

usetikzlibrary{calc,intersections}



usepackage{pgfplots}

pgfplotsset{compat=1.11}



setlength{oddsidemargin}{0.0in}

setlength{evensidemargin}{0.0in} setlength{textwidth}{6.1in}

setlength{topmargin}{0.0in} setlength{textheight}{9in}





begin{document}



noindent

begin{minipage}[t]{4.875in}raggedright

textbf{1.)} The following figure depicts three congruent semicircles 

bounded by another semicircle; the diameters of the three smaller 

semicircles cover the diameter of the bigger semicircle, and each of 

the three smaller semicircles is tangent to two other semicircles at 

the endpoints of its diameter. $A$ is the area of of the region 

enclosed by the three smaller semicircles and $B$ is the areapar

xdeftpd{theprevdepth}

end{minipage}hfill

raisebox{0mm}[0mm][0mm]{%

  begin{tikzpicture}[baseline=(current bounding box.north west)]



  coordinate (O) at (0,0);

  draw[fill=blue!50] (-1.5,0) -- (1.5,0) arc (0:180:1.5) -- cycle;

  %

  draw[fill=yellow] (-3/2,0) -- (-1/2,0) arc (0:180:1/2) -- cycle;

  draw[fill=yellow] (-1/2,0) -- (1/2,0) arc (0:180:1/2) -- cycle;

  draw[fill=yellow] (1/2,0) -- (3/2,0) arc (0:180:1/2) -- cycle;



  draw[fill] (O) circle (1.5pt);

  end{tikzpicture}

}



prevdepth=tpd

noindent

the region enclosed by the big semicircle but outside the three smaller 

semicircles. Compute the ratio of $A : B$.



bigskip



begin{wrapfigure}[4]{r}{3.2cm}

  vspace{-baselineskip}

  begin{tikzpicture}[baseline=(current bounding box.south west)]



  coordinate (O) at (0,0);

  draw[fill=blue!50] (-1.5,0) -- (1.5,0) arc (0:180:1.5) -- cycle;

  %

  draw[fill=yellow] (-3/2,0) -- (-1/2,0) arc (0:180:1/2) -- cycle;

  draw[fill=yellow] (-1/2,0) -- (1/2,0) arc (0:180:1/2) -- cycle;

  draw[fill=yellow] (1/2,0) -- (3/2,0) arc (0:180:1/2) -- cycle;



  draw[fill] (O) circle (1.5pt);

  end{tikzpicture}

end{wrapfigure}

noindent

textbf{1.)} The following figure depicts three congruent semicircles 

bounded by another semicircle; the diameters of the three smaller 

semicircles cover the diameter of the bigger semicircle, and each of 

the three smaller semicircles is tangent to two other semicircles at 

the endpoints of its diameter. $A$ is the area of of the region 

enclosed by the three smaller semicircles and $B$ is the area

the region enclosed by the big semicircle but outside the three smaller 

semicircles. Compute the ratio of $A : B$.



end{document}

it is not very clear to me what you like to obtain. see, if the my guessing is close to your goal:

for above result i use the wrapfig package:

documentclass[dvipsname]{amsart}

usepackage{tikz}

usetikzlibrary{calc, intersections}



usepackage{wrapfig}



begin{document}

begin{wrapfigure}{r}{0.25textwidth}

    begin{tikzpicture}

draw[fill=blue!50] (-1.5,0) -- (1.5,0) arc (0:180:1.5) -- cycle;

%

draw[fill=yellow] (-3/2,0) -- (-1/2,0) arc (0:180:1/2) -- cycle;

draw[fill=yellow] (-1/2,0) -- (1/2,0) arc (0:180:1/2) -- cycle;

draw[fill=yellow] (1/2,0) -- (3/2,0) arc (0:180:1/2) -- cycle;



draw[fill] (0,0) circle (1.5pt);

    end{tikzpicture}

end{wrapfigure}

noindenttextbf{1.)}

The following figure depicts three congruent semicircles bounded by another

semicircle; the diameters of the three smaller semicircles cover the diameter 

of the bigger semicircle, and each of the three smaller semicircles is tangent 

to two other semicircles at the endpoints of its diameter. $A$ is the area of

of the region enclosed by the three smaller semicircles and $B} is the area

the region enclosed by the big semicircle but outside the three smaller 

semicircles. Compute the ratio of $A : B$.

end{document}