Notes: `a = 8, b = 12, c = 17` Use Heron's Area Formula to find the area of the triangle.

Tuesday, 26 September 2017

Given: $\displaystyle{a}={8},{b}={12},{c}={17}$

Heron's Area Formula $\displaystyle{A}=\sqrt{{{s}{\left({s}-{a}\right)}{\left({s}-{b}\right)}{\left({s}-{c}\right)}}}$

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

$\displaystyle{s}=\frac{{{8}+{12}+{17}}}{{2}}=\frac{{37}}{{2}}={18.5}$

$\displaystyle{A}=\sqrt{{{18.5}{\left({18.5}-{8}\right)}{\left({18.5}-{12}\right)}{\left({18.5}-{17}\right)}}}$

$\displaystyle{A}=\sqrt{{{18.5}{\left({10.5}\right)}{\left({6.5}\right)}{\left({1.5}\right)}}}$

$\displaystyle{A}=\sqrt{{{1893.94}}}={43.52}$

The area is 43.52 square units.

Given: $\displaystyle{a}={8},{b}={12},{c}={17}$

Heron's Area Formula $\displaystyle{A}=\sqrt{{{s}{\left({s}-{a}\right)}{\left({s}-{b}\right)}{\left({s}-{c}\right)}}}$

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

$\displaystyle{s}=\frac{{{8}+{12}+{17}}}{{2}}=\frac{{37}}{{2}}={18.5}$

$\displaystyle{A}=\sqrt{{{18.5}{\left({18.5}-{8}\right)}{\left({18.5}-{12}\right)}{\left({18.5}-{17}\right)}}}$

$\displaystyle{A}=\sqrt{{{18.5}{\left({10.5}\right)}{\left({6.5}\right)}{\left({1.5}\right)}}}$

$\displaystyle{A}=\sqrt{{{1893.94}}}={43.52}$

The area is 43.52 square units.

Notes