Question

find the area of the triangle, carry your internediate computations to at least four decimal places round your answer to the nearest tenth

Answer 1

Heron's formula is defined as:

`\begin{gathered} A=\sqrt[]{s(s-a)(s-b)(s-c)} \\ \text{where} \\ a,b,\text{ and }c\text{ are the three sides of the triangle} \\ s=(a+b+c)/(2) \end{gathered}`

Given: sides with length 12 yd, 14 yd, 15 yd.

Then

`\begin{gathered} s=(12+14+15)/(2) \\ s=(41)/(2) \\ s=20.5\text{ yd} \end{gathered}`

Plugin the following values to Heron's formula and we get

`\begin{gathered} A=\sqrt[]{s(s-a)(s-b)(s-c)} \\ A=\sqrt[]{20.5(20.5-12)(20.5-14)(20.5-15)} \\ A=\sqrt[]{20.5(8.5)(6.5)(5.5)} \\ A=78.926785694085\text{ yd}^2 \\ \text{Rounded this off to the nearest tenth and we get} \\ A=78.9\text{ yd}^2 \end{gathered}`