Question

Find the area of the triangle described in Problem 5.

Short answer

The area of the triangle is$19.81$square units.

Step-by-step solution

Step 1. Given Information

The given triangle is

Step 2. Find the Semiperimeter

The semiperimeter of the triangle is$\begin{array}{rcl}s& =& \frac{5+8+10}{2}\\ & =& 11.5\end{array}$

Step 3. Find the Area

• The area of a triangle is given by the formula, $A=\sqrt{s(s-a)(s-b)(s-c)}$.
• Calculate the area.

$\begin{array}{rcl}A& =& \sqrt{11.5\times 6.5\times 3.5\times 1.5}\\ & =& \sqrt{392.4375}\\ & \approx & 19.81\end{array}$