document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1154447>Question 1154447</A>: <I><SPAN STYLE=\"word-break: break-all;\"> HI <BR>\n" );
document.write( "PLEASE HELP <BR>\n" );
document.write( "A right prism has a base in the shape of a right isosceles triangle with hypotenuse measuring 8.5 cm. The height of the prism is 12 cm. Round answers to the nearest ten.\r<BR>\n" );
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document.write( "(a) What is the volume?<BR>\n" );
document.write( "Base is in the form of a right isosceles triangle with hypotenuse = 8.5. Through Pythagoras theorem, we know that in a right isosceles triangle, the hypotenuse is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%282%29 ALIGN=MIDDLE  ALT=\"sqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > times the other side. Hence the two equal sides of the base triangle measure = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8.5+%2F+sqrt%282%29 ALIGN=MIDDLE  ALT=\"8.5+%2F+sqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 6.01 cm.<BR>\n" );
document.write( "Area of the base triangle = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.5+%2A+6.01+%2A+6.01+=+18.06 ALIGN=MIDDLE  ALT=\"0.5+%2A+6.01+%2A+6.01+=+18.06\"   DISABLED_style= \"max-width:90%; height:auto;\" >cm2<BR>\n" );
document.write( "Volume of the prism = base area * height = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=18.06+%2A+12+=+216.75+=+216.8 ALIGN=MIDDLE  ALT=\"18.06+%2A+12+=+216.75+=+216.8\"   DISABLED_style= \"max-width:90%; height:auto;\" > cm3 - rounded to nearest 10th decimal place\r<BR>\n" );
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document.write( "(b) What is the total surface area?<BR>\n" );
document.write( "Total surface area = 2 * area of base triangle + area of the 3 rectangles that form the vertical faces.<BR>\n" );
document.write( "Area of base triangle = 18.06 cm2 as calculated earlier<BR>\n" );
document.write( "Of the 3 vertical rectangles, all of them have the longer side as 12 cm (height of the prism). 2 of them have the shorter side as 6.01 cm and one has the shorter side as 8.5 cm. So the sum of the 3 areas is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12+%2A+6.01+%2B+12+%2A+6.01+%2B+12+%2A+8.5+=+246.25+cm2%0D%0ASo+the+total+surface+area+=+%7B%7B%7B18.06+%2A+2+%2B+246.25+=+282.4 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > cm2 (rounded off to nearest 10th decimal) </SPAN>\n" );
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document.write( "(a) What is the volume?<BR>\n" );
document.write( "Base is in the form of a right isosceles triangle with hypotenuse = 8.5. Through Pythagoras theorem, we know that in a right isosceles triangle, the hypotenuse is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%282%29 ALIGN=MIDDLE  ALT=\"sqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > times the other side. Hence the two equal sides of the base triangle measure = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8.5+%2F+sqrt%282%29 ALIGN=MIDDLE  ALT=\"8.5+%2F+sqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 6.01 cm.<BR>\n" );
document.write( "Area of the base triangle = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.5+%2A+6.01+%2A+6.01+=+18.06 ALIGN=MIDDLE  ALT=\"0.5+%2A+6.01+%2A+6.01+=+18.06\"   DISABLED_style= \"max-width:90%; height:auto;\" >cm2<BR>\n" );
document.write( "Volume of the prism = base area * height = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=18.06+%2A+12+=+216.75+=+216.8 ALIGN=MIDDLE  ALT=\"18.06+%2A+12+=+216.75+=+216.8\"   DISABLED_style= \"max-width:90%; height:auto;\" > cm3 - rounded to nearest 10th decimal place\r<BR>\n" );
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document.write( "(b) What is the total surface area?<BR>\n" );
document.write( "Total surface area = 2 * area of base triangle + area of the 3 rectangles that form the vertical faces.<BR>\n" );
document.write( "Area of base triangle = 18.06 cm2 as calculated earlier<BR>\n" );
document.write( "Of the 3 vertical rectangles, all of them have the longer side as 12 cm (height of the prism). 2 of them have the shorter side as 6.01 cm and one has the shorter side as 8.5 cm. So the sum of the 3 areas is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12+%2A+6.01+%2B+12+%2A+6.01+%2B+12+%2A+8.5+=+246.25+cm2%0D%0ASo+the+total+surface+area+=+%7B%7B%7B18.06+%2A+2+%2B+246.25+=+282.4 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > cm2 (rounded off to nearest 10th decimal) </SPAN>\n" );
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