document.write( "Question 581522: How many different ways can you find the area of a regular octagon with all sides equal to 3 meters? Describe each method and use it to find the area. Are the answers the same? Should the answers be the same? \n" ); document.write( "

Algebra.Com's Answer #371906 by richard1234(7193) $\"\"$ $\"About$

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Suppose the vertices of the octagon are A,B,C,...,H in counterclockwise order with AB = 3 m, and O is the center.\r
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\n" ); document.write( "\n" ); document.write( "1. Divide up the octagon into four triangles and five rectangles (draw lines AF, BE, CH, DG). Find the area of each shape using your knowledge about 45-45-90 triangles.\r
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\n" ); document.write( "\n" ); document.write( "2. Think of the octagon as a square with four right isosceles triangles cut off. Find the area of the square, then subtract off the areas of the triangles.\r
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\n" ); document.write( "\n" ); document.write( "3. Divide up the octagon into eight congruent isosceles triangles (OAB, OBC, etc.). Use the area formula A = (1/2)ab sin C where a = b = the radius of the circumscribed circle, and C = 45 deg. You may need additional theorems, such as law of sines.\r
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\n" ); document.write( "\n" ); document.write( "There are many other ways, but most of them are similar to the above three. You should obtain the same answer in each case. \n" ); document.write( "

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