Chapter 12.9, Problem 5OE

To determine

Find the formula for area of triangle ABC such that $a=12,b=8\text{ and }c=12$ .

Answer to Problem 5OE

The formula for area $\left(A\right)$ of triangle ABC is $A=\sqrt{s\left(s-a\right)\left(s-b\right)\left(s-c\right)}\mathrm{....}\left(\text{where }s=\frac{a+b+c}{2}\right)$ .

Explanation of Solution

Given information: The given triangle ABC has $a=12,b=8\text{ and }c=12$ .

Calculation: Since the given triangle ABC has $a=12,b=8\text{ and }c=12$ . And the given triangle has the case of side-side-side where no angle is mentioned. Therefore the formula for area $\left(A\right)$ of triangle ABC is given by the Hero’s formula,

  $A=\sqrt{s\left(s-a\right)\left(s-b\right)\left(s-c\right)}\mathrm{....}\left(\text{where }s=\frac{a+b+c}{2}\right)$