Answer:
9 square meters
Step-by-step explanation:
Heron's formula first tells us how to find the semi-perimeter, S, given sides A, B and C:
[tex]S=\frac{A+B+C}{2}[/tex]
Next we are told how to find the area:
[tex]\text{Area}=\sqrt{S(S-A)(S-B)(S-C)}[/tex]
We know that the perimeter, or distance around all three sides, is 16. Letting x represent the unknown side, this gives us
16 = 7+6+x
16 = 13+x
Subtracting 13 from each side, we have
16-13 = 13+x-13
3 = x
Next we find the semi-perimeter:
[tex]S=\frac{7+6+3}{2}=\frac{16}{2}=8[/tex]
Lastly we use these to find the area:
[tex]\text{Area}=\sqrt{8(8-7)(8-6)(8-3)}=\sqrt{8(1)(2)(5)}\\\\=\sqrt{80}=8.94\approx 9[/tex]
