document.write( "Question 558597: Could you please help with question I cannot copy it because of a picture you will have to see here is the website http://www.analyzemath.com/middle_school_math/grade_8/problems.html
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Algebra.Com's Answer #363131 by Edwin McCravy(20086) $\"\"$ $\"About$

You can put this solution on YOUR website!

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document.write( "The size of the perimeter of the square ABCD is equal to 100 cm. The length of\r\n" );
document.write( "the segment MN is equal to 5 cm and the triangle MNC is isosceles. Find the\r\n" );
document.write( "area of the pentagon ABNMC.\r\n" );
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document.write( "(The picture on that site isn't to scale.  This is.)\r\n" );
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document.write( "The square's perimeter is 100 cm, so each side of the square is 25 cm.\r\n" );
document.write( "The area of the square is (25 cm)² or 625 cm²\r\n" );
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document.write( "We need to subtract the area of the triangle.  It is a right triangle, and\r\n" );
document.write( "it isosceles, so MC = CN.  We use the Pythagorean theorem to find MC and CN.\r\n" );
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document.write( "MC² + CN² = MN²\r\n" );
document.write( "MC² + MC² = 5²\r\n" );
document.write( "     2MC² = 25\r\n" );
document.write( "      MC² = 12.5\r\n" );
document.write( "       MC =  = CN\r\n" );
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document.write( "Area of the triangle = BASE×HEIGHT = MC×CN = × =  = (12.5) = 6.25 cm²\r\n" );
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document.write( "Area of pentagon = Area of square - Area of triangle\r\n" );
document.write( "                 = 625 cm² - 6.25 cm² = 618.75 cm²\r\n" );
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document.write( "I won't draw the other one.\r\n" );
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document.write( "Initially the rectangular prism on the left was full of water. \r\n" );
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document.write( "It measures 2cm×4cm×10cm\r\n" );
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document.write( "Volume = length × width × height = 2cm × 4cm × 10cm = 80cm³\r\n" );
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document.write( "so the volume of water in the original container is 80cm³\r\n" );
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document.write( "The first container into which part of it was poured to a height of h\r\n" );
document.write( "is a rectangular prism like the original except that it is only\r\n" );
document.write( "filled to a height of h cm.\r\n" );
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document.write( "Volume of water = length × width × height = 2cm × 4cm × h cm = 8h cm³\r\n" );
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document.write( "The second container into which the other part of it was poured to a height \r\n" );
document.write( "of h cm is a cylinder with radius 1 cm.\r\n" );
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document.write( "Volume of water = p × (radius)² × (height) = p(1)²h = ph = (3.14)h\r\n" );
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document.write( "so the volume of water in the cylinder is 3.14h cm³.\r\n" );
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document.write( "           water in original = water in 1st + water in 2nd \r\n" );
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document.write( "                          80 = 8h + 3.14h\r\n" );
document.write( "                          80 = 11.14h\r\n" );
document.write( "                          = h\r\n" );
document.write( "                         7.2 = h\r\n" );
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document.write( " So the height is 7.2 cm to the nearest tenth of a centimeter.    \r\n" );
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document.write( "Edwin

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