Question

Find the area of the triangle. If you get this right I will mark you as a brainliest

Answer 1

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.