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

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=√(s(s-a)(s-b)(s-c)) \\ where\text{ } \\ s=(a+b+c)/(2) \end{gathered}`

So, s becomes

`\begin{gathered} s=(a+b+c)/(2) \\ s=(18.6+18.3+13.5)/(2) \\ s=(50.4)/(2) \\ s=25.2 \end{gathered}`

Area becomes

`\begin{gathered} Area=√(s(s-a)(s-b)(s-c)) \\ Area=√(25.2(25.2-18.6)(25.2-18.3)(25.2-13.5)) \\ Area=√(25.2*6.6*6.9*11.7) \\ Area=√(13,427.0136) \\ Area=115.87499 \\ Area=116\text{ cm}^2 \end{gathered}`

Hence the answer is option D