We can use Heron's formula to determine the area of a triangle when given the lengths of the sides.
Heron's formula
[tex]\begin{gathered} A=\sqrt{s\left(s-a\right?\left(s-b\right)\left(s-c\right)} \\ \text{ where} \\ s=\frac{a+b+c}{2} \end{gathered}[/tex]
where a, b, and c are the lengths of the sides.
Substituting with b = 29, a = 20, and c = 17, the area of the triangle is:
[tex]\begin{gathered} s=\frac{20+29+17}{2} \\ s=33 \\ A=\sqrt{33\left(33-20\right)\left(33-29\right)\left(33-17\right)} \\ A=\sqrt{33\cdot13\cdot4\cdot16} \\ A=\sqrt{27456} \\ A\approx165.70 \end{gathered}[/tex]
