{"status": "success", "data": {"description_md": "Points $K, L, M,$ and $N$ lie in the plane of the square $ABCD$ such that $AKB$, $BLC$, $CMD$, and $DNA$ are equilateral triangles. If $ABCD$ has an area of 16, find the area of $KLMN$.<br><center><img class=\"problem-image\" alt='[asy] unitsize(2cm); defaultpen(fontsize(8)+linewidth(0.8)); pair A=(-0.5,0.5), B=(0.5,0.5), C=(0.5,-0.5), D=(-0.5,-0.5); pair K=(0,1.366), L=(1.366,0), M=(0,-1.366), N=(-1.366,0); draw(A--N--K--A--B--K--L--B--C--L--M--C--D--M--N--D--A); label(\"$A$\",A,SE); label(\"$B$\",B,SW); label(\"$C$\",C,NW); label(\"$D$\",D,NE); label(\"$K$\",K,NNW); label(\"$L$\",L,E); label(\"$M$\",M,S); label(\"$N$\",N,W); [/asy]' class=\"latexcenter\" height=\"288\" src=\"https://latex.artofproblemsolving.com/1/4/0/14057a8f4f08bad17471fdaed56a758f1e2fcea7.png\" width=\"295\"/></center>\n\n$\\textrm{(A)}\\ 32\\qquad\\textrm{(B)}\\ 16+16\\sqrt{3}\\qquad\\textrm{(C)}\\ 48\\qquad\\textrm{(D)}\\ 32+16\\sqrt{3}\\qquad\\textrm{(E)}\\ 64$\n___\nFull credit goes to [MAA](https://maa.org/) for authoring these problems. These problems were taken on the [AOPS](https://artofproblemsolving.com/) website.", "description_html": "<p>Points  <span class=\"katex--inline\">K, L, M,</span>  and  <span class=\"katex--inline\">N</span>  lie in the plane of the square  <span class=\"katex--inline\">ABCD</span>  such that  <span class=\"katex--inline\">AKB</span> ,  <span class=\"katex--inline\">BLC</span> ,  <span class=\"katex--inline\">CMD</span> , and  <span class=\"katex--inline\">DNA</span>  are equilateral triangles. If  <span class=\"katex--inline\">ABCD</span>  has an area of 16, find the area of  <span class=\"katex--inline\">KLMN</span> .<br/><center><img class=\"latexcenter\" alt=\"[asy] unitsize(2cm); defaultpen(fontsize(8)+linewidth(0.8)); pair A=(-0.5,0.5), B=(0.5,0.5), C=(0.5,-0.5), D=(-0.5,-0.5); pair K=(0,1.366), L=(1.366,0), M=(0,-1.366), N=(-1.366,0); draw(A--N--K--A--B--K--L--B--C--L--M--C--D--M--N--D--A); label(&#34;$A$&#34;,A,SE); label(&#34;$B$&#34;,B,SW); label(&#34;$C$&#34;,C,NW); label(&#34;$D$&#34;,D,NE); label(&#34;$K$&#34;,K,NNW); label(&#34;$L$&#34;,L,E); label(&#34;$M$&#34;,M,S); label(&#34;$N$&#34;,N,W); [/asy]\" height=\"288\" src=\"https://latex.artofproblemsolving.com/1/4/0/14057a8f4f08bad17471fdaed56a758f1e2fcea7.png\" width=\"295\"/></center></p>&#10;<p> <span class=\"katex--inline\">\\textrm{(A)}\\ 32\\qquad\\textrm{(B)}\\ 16+16\\sqrt{3}\\qquad\\textrm{(C)}\\ 48\\qquad\\textrm{(D)}\\ 32+16\\sqrt{3}\\qquad\\textrm{(E)}\\ 64</span> </p>&#10;<hr><p>Full credit goes to <a href=\"https://maa.org/\">MAA</a> for authoring these problems. These problems were taken on the <a href=\"https://artofproblemsolving.com/\">AOPS</a> website.</p>", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 3, "problem_name": "2003 AMC 12A Problem 14", "can_next": true, "can_prev": true, "nxt": "/problem/03_amc12A_p15", "prev": "/problem/03_amc12A_p13"}}