Question

Find the area of a triangle with sides a=5, b=8, and c=11. use herons formula.

Answer 1

Step-by-step explanation:

The given sides of the triangle is given below as

`\begin{gathered} a=5 \\ b=8 \\ c=11 \end{gathered}`

The heron's formula is given below as

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

By substituting the values, we will have

`\begin{gathered} s=(a+b+c)/(2) \\ s=(5+8+11)/(2) \\ s=(24)/(2) \\ s=12 \end{gathered}`

Hence,

The area of the triangle will be

`\begin{gathered} A=√(s(s-a)(s-b)(s-c)) \\ A=√(12(12-5)(12-8)(12-11)) \\ A=√(12(7*4*1)) \\ A=√(336) \\ A=18.33 \end{gathered}`

Hence,

The final answer is

`\Rightarrow18.33`