A kite in the shape of a square with a diagonal 32 cm and an isoscales triangle of base 8 cm and side 6 cm each is to be made of three different shades as shown in figure. How much paper of each shade has been used in it?

Solution

Area of paper of shade I

equals 1 half open parentheses 1 half cross times 32 cross times 32 close parentheses equals 256 space cm squared

Area of paper of shade II = 256 cm² For paper of shade III
a = 8 cm b = 6 cm c = 6 cm
$therefore space space space space straight s equals fraction numerator straight a plus straight b plus straight c over denominator 2 end fraction equals fraction numerator 8 plus 6 plus 6 over denominator 2 end fraction equals 10 space cm$
$therefore space space space Area space of space paper space of space shade space III. equals square root of straight s left parenthesis straight s minus straight a right parenthesis left parenthesis straight s minus straight b right parenthesis left parenthesis straight s minus straight c right parenthesis end root equals square root of 10 left parenthesis 10 minus 8 right parenthesis left parenthesis 10 minus 6 right parenthesis left parenthesis 10 minus 6 right parenthesis end root equals space square root of 10 left parenthesis 2 right parenthesis left parenthesis 4 right parenthesis left parenthesis 4 right parenthesis end root equals 8 square root of 5 equals 17.92 space cm squared$

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Statistics

A kite in the shape of a square with a diagonal 32 cm and an isoscales triangle of base 8 cm and side 6 cm each is to be made of three different shades as shown in figure. How much paper of each shade has been used in it?

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