Question

xCarry your intermediate computations to at least four decimal places. Round your answer to the nearest tenth.

Answer 1

Given

sides 17 ft, 14 ft, and 20 ft.

Recall that given three sides of a triangle, we can calculate the area using Heron's Formula which states that

$\begin{gathered} A=\sqrt{s(s-a)(s-b)(s-c)} \\ \text{where} \\ a,b,\text{ and }c\text{ are the length of the sides of a triangle} \\ s\text{ is }\frac{a+b+c}{2} \end{gathered}$

Solve for s first and we get

$\begin{gathered} s=\frac{a+b+c}{2} \\ s=\frac{14+17+20}{2} \\ s=\frac{51}{2} \\ s=25.5 \end{gathered}$

Next, use Heron's formula and we have

$\begin{gathered} A=\sqrt{s(s-a)(s-b)(s-c)} \\ A=\sqrt{25.5(25.5-14)(25.5-17)(25.5-20)} \\ A=\sqrt{25.5\cdot11.5\operatorname{\cdot}8.5\operatorname{\cdot}5.5} \\ A=\sqrt{13709.4375} \\ A=117.0873 \end{gathered}$

Rounding our final answer to the nearest tenth, the area of the given triangle is 117.1 square feet.