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:

$A_S=\frac{base\cdot height}{2}$

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:

$s=\frac{a+b+c}{2}$

Let's find s:

$s=\frac{12+16+25}{2}$$s=\frac{53}{2}$

Then, replace s on the area formula:

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

Hence, the area of the triangle given is:

$A=77.8$

The value is rounded to the nearest tenth.