Question

If a = 12, b = 16, and c = 25, then the area of triangle ABC = ….

Answer 1

The area of a triangle is given by the next formula:

`A_S=(base\cdot height)/(2)`

Now, in this case, we don't know the height. Therefore, we need to use Heron's formula:

`A_S=\sqrt[]{s(s-a)\cdot(s-b)\cdot(s-c)}`

Where s:

`s=(a+b+c)/(2)`

Let's find s:

`s=(12+16+25)/(2)`
`s=(53)/(2)`

Then, replace s on the area formula:

`A=\sqrt[]{((53)/(2)((53)/(2)-12)\cdot((53)/(2)-16)\cdot((53)/(2)-25))}`

Hence, the area of the triangle given is:

`A=77.8`

The value is rounded to the nearest tenth.