document.write( "Question 1101878: Triangle ABC is an equilateral triangle with sides of length 3 cm. AB, AC, and BC are arcs of circles having their centres at C, B, and A respectively. Find the total area of the non-shaded region (the area of the triangle itself, not including the arcs), in cm^2. \n" ); document.write( "

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\n" ); document.write( "If the drawing above is what the figure is supposed to look like,
\n" ); document.write( "the arcs have a radius of $\"r=3cm%2F2=1.5cm\"$ .
\n" ); document.write( "Each angle in an equilateral triangle is
\n" ); document.write( " $\"60%5Eo\"$ or $\"1%2F6\"$ of a whole turn,
\n" ); document.write( "so the total area of the 3 circle sectors
\n" ); document.write( "is half a circle of radius $\"1.5cm\"$ ,
\n" ); document.write( "or $\"pi%2A1.5%5E2%2F2\"$ $\"cm%5E2=1.125pi\"$ $\"cm%5E2\"$ .
\n" ); document.write( "The area of an equilateral triangle can be calculated as
\n" ); document.write( " $\"sqrt%283%29side%5E2%2F4\"$ ,
\n" ); document.write( "so the area of the whole triangle in the problem is
\n" ); document.write( " $\"sqrt%283%29%283cm%29%5E2%2F4=2.25sqrt%283%29\"$ $\"cm\"$ .
\n" ); document.write( "The area of the triangle minus the 3 sectors is
\n" ); document.write( " $\"2.25sqrt%283%29-1.125pi\"$ $\"cm%5E2=approximately\"$ $\"0.3627cm%5E2\"$ \n" ); document.write( "

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