Question

Find the area of triangle ABC with the given parts. Round to the nearest tenth when necessary.a=18.6cmb=18.3cmc=13.5cmOption 1: 122 cm^2Option 2: 125 cm^2Option 3: 119 cm^2Option 4: 116 cm^2

Answer 1

SOLUTION

From the question we want to find the area of a triangle ABC with sides

a = 18.6cm, b = 18.3cm, c = 13.5cm

To do this we will apply the Heroes formula. From Heroes formula, we have

$\begin{gathered} Area=\sqrt{s(s-a)(s-b)(s-c)} \\ where\text{ } \\ s=\frac{a+b+c}{2} \end{gathered}$

So, s becomes

$\begin{gathered} s=\frac{a+b+c}{2} \\ s=\frac{18.6+18.3+13.5}{2} \\ s=\frac{50.4}{2} \\ s=25.2 \end{gathered}$

Area becomes

$\begin{gathered} Area=\sqrt{s(s-a)(s-b)(s-c)} \\ Area=\sqrt{25.2(25.2-18.6)(25.2-18.3)(25.2-13.5)} \\ Area=\sqrt{25.2\times6.6\times6.9\times11.7} \\ Area=\sqrt{13,427.0136} \\ Area=115.87499 \\ Area=116\text{ cm}^2 \end{gathered}$

Hence the answer is option D