Notes: `a = 12.32, b = 8.46, c = 15.05` Use Heron's Area Formula to find the area of the triangle.

Monday, 21 March 2016

$\displaystyle{a}={12.32},{b}={8.46},{c}={15.05}$ Use Heron's Area Formula to find the area of the triangle.

When the three sides of the triangle are known, its area can be solved using the Heron's formula.

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

where a, b and c are the length of the three sides and s is half of the triangle's perimeter.

The value of s will be:

$\displaystyle{s}=\frac{{{a}+{b}+{c}}}{{2}}=\frac{{{12.32}+{8.46}+{15.05}}}{{2}}=\frac{{35.83}}{{2}}={17.915}$

Plugging the values of s, a, b and c to the Heron's formula yields:

$\displaystyle{A}=\sqrt{{{17.915}{\left({17.915}-{12.32}\right)}{\left({17.915}-{8.46}\right)}{\left({17.915}-{15.05}\right)}}}$

$\displaystyle{A}={52.11}$

Therefore, the area of the triangle is 52.11 square units.

When the three sides of the triangle are known, its area can be solved using the Heron's formula.

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

where a, b and c are the length of the three sides and s is half of the triangle's perimeter.

The value of s will be:

$\displaystyle{s}=\frac{{{a}+{b}+{c}}}{{2}}=\frac{{{12.32}+{8.46}+{15.05}}}{{2}}=\frac{{35.83}}{{2}}={17.915}$

Plugging the values of s, a, b and c to the Heron's formula yields:

$\displaystyle{A}=\sqrt{{{17.915}{\left({17.915}-{12.32}\right)}{\left({17.915}-{8.46}\right)}{\left({17.915}-{15.05}\right)}}}$

$\displaystyle{A}={52.11}$

Therefore, the area of the triangle is 52.11 square units.

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