Area of SSS Triangle- Heron’s Formula

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Notes

Notes for Heron's Formula


Questions

\(\hspace{-12pt}\small{\textbf{1)}}\)Find the area of this triangle.
Triangle for Question Number 1Link to Youtube Video Solving Question Number 1



\(\hspace{-12pt}\small{\textbf{2)}}\) Find the area of this triangle.
Triangle for Question Number 2


\(\hspace{-12pt}\small{\textbf{3)}}\)Find the area of this triangle.
Triangle for Question Number 3



\(\hspace{-12pt}\small{\textbf{4)}}\)Find the area of this triangle.
Triangle for Question Number 4



\(\hspace{-12pt}\small{\textbf{5)}}\)Find the area of this triangle.
Triangle for Question Number 5



See Related Pages\(\)

\(\bullet\text{ Geometry Homepage}\)
\(\,\,\,\,\,\,\,\,\text{All the Best Topics…}\)
\(\bullet\text{ Triangle Calculator (Calculator.net)}\)
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\(\bullet\text{ Law of Cosines}\)
\(\,\,\,\,\,\,\,\,a^2=b^2+c^2-2bc \cos{A}\) Thumbnail for Law of Cosines\(…\)
\(\bullet\text{ Area of SSS Triangles (Heron’s formula)}\)
\(\,\,\,\,\,\,\,\,\text{Area}=\sqrt{s(s-a)(s-b)(s-c)}\) Thumbnail for Heron's Formula\(…\)
\(\bullet\text{ Geometric Mean}\)
\(\,\,\,\,\,\,\,\,x=\sqrt{ab} \text{ or } \displaystyle\frac{a}{x}=\frac{x}{b}…\)
\(\bullet\text{ Geometric Mean- Similar Right Triangles}\)
\(\,\,\,\,\,\,\,\,\)Thumbnail for Similar Right Triangles\(…\)
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\(\,\,\,\,\,\,\,\,\sin{(2A)}=2\sin{(A)}\cos{(A)}…\)
\(\bullet\text{ Trigonometry-Pythagorean Identities}\)
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\(\bullet\text{ Product-Sum Identities}\)
\(\,\,\,\,\,\,\,\,\cos{\alpha}\cos{\beta}=\left(\displaystyle\frac{\cos{(\alpha+\beta)}+\cos{(\alpha-\beta)}}{2}\right)…\)
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\(\bullet\text{ Andymath Homepage}\)

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In Summary

Heron’s formula is a process for finding the area of any triangle where all 3 sides are known. It works on right-angled, obtuse and acute triangles.
It’s named after an ancient Greek mathematician Heron of Alexandria.

Heron’s formula is typically introduced in a high school geometry course while learning about triangles.

One common mistake students make when working with Heron’s formula is to forget to divide the sum of the sides by 2 to get the semiperimeter. The formula doesn’t work if you use the entire perimeter.

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