Question 1143340
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Heron's formula gives the area of a triangle in terms of the lengths of the three sides:<br>
{{{A = sqrt(s(s-a)(s-b)(s-c))}}}<br>
where s is the semiperimeter.<br>
The formula looks scary; but it is easy to use.<br>
(1) find the semiperimeter: {{{s = (a+b+c)/2 = (4+13+15)/2 = 16}}}
(2) find the differences between the semiperimeter and each side: {{{s-a = 16-4 = 12}}}; {{{s-b = 16-13 = 3}}}; {{{s-c = 16-15 = 1}}}
(3) evaluate: {{{A = sqrt(16*12*3*1) = sqrt(16*36*1) = 4*6 = 24}}}<br>
The area of the triangle is 24 square units.