Heron's formula is defined as:
[tex]\begin{gathered} A=\sqrt[]{s(s-a)(s-b)(s-c)} \\ \text{where} \\ a,b,\text{ and }c\text{ are the three sides of the triangle} \\ s=\frac{a+b+c}{2} \end{gathered}[/tex]
Given: sides with length 12 yd, 14 yd, 15 yd.
Then
[tex]\begin{gathered} s=\frac{12+14+15}{2} \\ s=\frac{41}{2} \\ s=20.5\text{ yd} \end{gathered}[/tex]
Plugin the following values to Heron's formula and we get
[tex]\begin{gathered} A=\sqrt[]{s(s-a)(s-b)(s-c)} \\ A=\sqrt[]{20.5(20.5-12)(20.5-14)(20.5-15)} \\ A=\sqrt[]{20.5(8.5)(6.5)(5.5)} \\ A=78.926785694085\text{ yd}^2 \\ \text{Rounded this off to the nearest tenth and we get} \\ A=78.9\text{ yd}^2 \end{gathered}[/tex]
