document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1197252>Question 1197252</A>: <I><SPAN STYLE=\"word-break: break-all;\"> find the are of a quadrilateral having points (5,2), (4,3), (2,4), (-8,-1) as consecutive vertices. </SPAN>\n" );
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document.write( "Plot the given points and form a quadrilateral by joining up adjacent vertices<BR>\n" );
document.write( "Eg: (5,2) connects to (4,3)\r<BR>\n" );
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document.write( "After doing that, mark lattice points on the boundary and lattice points inside the polygon.<BR>\n" );
document.write( "A lattice point has both coordinates as integer values. It's where the dashed grid lines intersect.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src = \"https://i.imgur.com/qzlE9Cl.png\"><BR>\n" );
document.write( "Each point marked has integer coordinates x,y<BR>\n" );
document.write( "Red points are on the boundaries<BR>\n" );
document.write( "Blue points are interior\r<BR>\n" );
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document.write( "b = number of boundary lattice points = number of red points = 8<BR>\n" );
document.write( "i = number of interior lattice points = number of blue points = 15\r<BR>\n" );
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document.write( "Use Pick's Theorem<BR>\n" );
document.write( "<a  rel=nofollow HREF= \"https://mathworld.wolfram.com/PicksTheorem.html\">https://mathworld.wolfram.com/PicksTheorem.html</a><BR>\n" );
document.write( "<a  rel=nofollow HREF= \"https://en.wikipedia.org/wiki/Pick%27s_theorem\">https://en.wikipedia.org/wiki/Pick%27s_theorem</a><BR>\n" );
document.write( "to get this<BR>\n" );
document.write( "A = area of the polygon<BR>\n" );
document.write( "A = i + 0.5*b - 1<BR>\n" );
document.write( "A = 15 + 0.5*8 - 1<BR>\n" );
document.write( "A = 15 + 4 - 1<BR>\n" );
document.write( "A = 19 - 1<BR>\n" );
document.write( "A = 18\r<BR>\n" );
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document.write( "Answer: The area of the quadrilateral is 18 square units\r<BR>\n" );
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document.write( "Keep in mind that Pick's Theorem only applies if all vertex or corner points are lattice points.\r<BR>\n" );
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document.write( "Another approach you could use is the shoelace formula (see this <a  rel=nofollow HREF=\"https://www.algebra.com/algebra/homework/Parallelograms/Parallelograms.faq.question.1204418.html\">example problem</a> )<BR>\n" );
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