document.write( "Question 203379: 4.if the apothem of a regular octagon is a and its side is b, express the areas in terms of a and b. \n" ); document.write( "

Algebra.Com's Answer #153459 by Earlsdon(6294) $\"\"$ $\"About$

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\n" ); document.write( "If you were to draw all of the diagonals in the regular octagon, you would see that the octagon would be divided into eight congruent isosceles triangles.
\n" ); document.write( "The base of each of these triangles is the side of the octagon, or b.
\n" ); document.write( "The height of each of these triangles is the apothem, or a.
\n" ); document.write( "The apothem is really just the radius of the inscribed circle of the octagon.
\n" ); document.write( "Now the area of each isosceles triangle is given by:
\n" ); document.write( " $\"A+=+%281%2F2%29bh\"$ but in this problem, h = a(the apothem) and b = b(the side), so we have:
\n" ); document.write( " $\"A+=+%281%2F2%29ab\"$ but since there are eight of these triangles in the entire octagon, the area of the octagon can be expressed, in terms of a and b, as:
\n" ); document.write( " $\"A+=+8%281%2F2%29ab\"$
\n" ); document.write( " $\"highlight%28A+=+4ab%29\"$ \n" ); document.write( "

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