Question 1147733
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The smaller triangle hypotenuse is  {{{sqrt(8^2 + 12^2)}}} = {{{sqrt(208)}}} cm.


The similarity coefficient from the larger triangle to the smaller triangle is, therefore, {{{20/sqrt(208)}}}.


The area of the larger triangle is then  {{{(20/sqrt(208))^2}}} = {{{400/208}}} = {{{25/13}}}  times the area of the smaller triangle.


<U>ANSWER</U>.  The area of the larger triangle is  {{{(1/2)*8*12*(25/13)}}} = {{{1200/13}}} = 92.31 square centimeters, approximately 
         (with 2 correct decimal places)
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Solved.