document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1198259>Question 1198259</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How many square inches are there in the lateral surface of a regular octagonal pyramid with 12 and 18 inches basal and lateral edges. Round off the answer to the nearest integer. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #848322 by </B><A HREF=/tutors/aboutme.mpl?userid=CPhill><B>CPhill(1959)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=CPhill><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=CPhill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=848322\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> **1. Find the Slant Height**\r<BR>\n" );
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document.write( "* We can use the Pythagorean theorem to find the slant height (the height of each triangular face of the pyramid).<BR>\n" );
document.write( "* Imagine a right triangle formed by:<BR>\n" );
document.write( "    * The base: Half the base edge of the octagon (12 inches / 2 = 6 inches)<BR>\n" );
document.write( "    * The height: The slant height (which we'll call 's')<BR>\n" );
document.write( "    * The hypotenuse: The lateral edge (18 inches)\r<BR>\n" );
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document.write( "* Using Pythagorean Theorem: <BR>\n" );
document.write( "    * s² = 18² - 6² <BR>\n" );
document.write( "    * s² = 324 - 36 <BR>\n" );
document.write( "    * s² = 288 <BR>\n" );
document.write( "    * s = √288 <BR>\n" );
document.write( "    * s ≈ 16.97 inches\r<BR>\n" );
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document.write( "**2. Calculate the Area of One Triangular Face**\r<BR>\n" );
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document.write( "* Area of a triangle = (1/2) * base * height<BR>\n" );
document.write( "* Area of one triangular face = (1/2) * base edge * slant height<BR>\n" );
document.write( "* Area of one triangular face = (1/2) * 12 inches * 16.97 inches ≈ 101.82 square inches\r<BR>\n" );
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document.write( "**3. Calculate the Lateral Surface Area**\r<BR>\n" );
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document.write( "* The octagonal pyramid has 8 triangular faces.<BR>\n" );
document.write( "* Lateral Surface Area = 8 * Area of one triangular face<BR>\n" );
document.write( "* Lateral Surface Area = 8 * 101.82 square inches ≈ 814.58 square inches\r<BR>\n" );
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document.write( "**4. Round to the Nearest Integer**\r<BR>\n" );
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document.write( "* Lateral Surface Area ≈ 815 square inches\r<BR>\n" );
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document.write( "**Therefore, the lateral surface area of the regular octagonal pyramid is approximately 815 square inches.**<BR>\n" );
document.write( " </SPAN>\n" );
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