While a triangle's area is often given as 1/2 times base times height, that requires a right triangle. The one in the picture is not a right triangle, so the height can't be found directly.
Fortunately, Heron's Formula works well here.
A = \sqrt{s(s-a)(s-b)(s-c)},
where s is the semiperimeter of the triangle; that is,
{\displaystyle s={\frac {a+b+c}{2}}.} s=\frac{a+b+c}{2}.[2]
The perimeter of the triangle is 6 + 5 + 7 = 18, so its semiperimeter is 9 (half of it).
Then, by Heron's Formula,
A = √(9)(9-5)(9-6)(9-7)
A = √(9)(4)(3)(2)
A = √216
A = √36 * √6 by breaking a root into a product of factors
A = 6 √6
As a decimal, 6√6 is, to one place, 14.7
So the area is 14.7 square kilometers and we should select choice A.
