Question

Find the area of a triangle ABC when c = 15 m, a = 20 meters, and b = 10 meters.

Answer 1

Recall Heron's Formula to find the area of a triangle with sides a, b and c.

We define a new quantity s given by:

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

Then, the area of the triangle is given by the formula:

$A=\sqrt{s(s-a)(s-b)(s-c)}$

For a=20, b=10 and c=15 we have:

$s=\frac{20+10+15}{2}=22.5$

Then, the area of the triangle is:

$\begin{gathered} A=\sqrt{22.5(22.5-20)(22.5-10)(22.5-15)} \\ =\sqrt{22.5(2.5)(12.5)(7.5)} \\ =\frac{75\sqrt{15}}{4} \\ =72.61843774... \\ \approx72.6 \end{gathered}$

Therefore, the exact answer is:

$A=\frac{75\sqrt{15}}{4}$

And the approximate area of the triangle ABC when c=15m, a=20m and b=10m is 72.6 m^2.