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title: Area of a Triangle
---
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## Area of a Triangle
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A triangle is a three sided, two dimensional polygon. There are three methods to determine the area.
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### Method 1
The area of a triangle can be calculated by multiplying 0.5 to the base length to the perpendicular height.
![Triangle-1 ](https://github.com/uuykay/misc/blob/master/area-triangle-image-2.jpg )
Mathematically this is expressed as:
![Formula-1 ](https://github.com/uuykay/misc/blob/master/triangle-equation-area-1.jpg )
### Method 2
If the perpendicular height is not known, you can use a different method to calculate the area. If you know the length of two sides and the size of the angle in between them, then the area can be found.
![Triangle-2 ](https://github.com/uuykay/misc/blob/master/area-triangle-image-3.jpg )
Mathematically this is expressed as:
![Formula-2 ](https://github.com/uuykay/misc/blob/master/triangle-equation-area-2.jpg )
Note that the formula expressed above uses sides a and b and angle C between them. These can be substituted for another other two sides and the angle between them.
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### Method 3
If only the length of the sides are known, we can use what is known as Heron's formula to find the area.
![Triangle-3 ](https://github.com/uuykay/misc/blob/master/area-triangle-image-3.jpg )
Mathematically this is expressed as:
![Formula-3 ](https://wikimedia.org/api/rest_v1/media/math/render/svg/d138044bb9ed870dd9dc5c7c8a3c07ab1db1705d )
Where s is half the perimeter, or
![Formula-3.1 ](https://wikimedia.org/api/rest_v1/media/math/render/svg/08ed8a6e351198e0c4ca8d71fa2e2bc4171e9439 )
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### Terminology
Base - The bottom side. Select a side that is known.
Perpendicular Height - The height of the triangle, measured perpendicular to the base, to the tallest point of the triangle.
Sin - The sine trigonometric expression.
### Examples
1. Find the area of a triangle with a base length of 4 units and a perpendicular height of 12 units
Area = 0.5 x 4 x 12 = 24 units< sup > 2< / sup >
2. If two sides of a triangle are known to be 3 and 6, and the angle between them is 30 degrees, what is the angle of the triangle?
Area = 0.5 x 3 x 6 x sin(30 degrees) = 4.5 units< sup > 2< / sup >
#### More Information:
<!-- Please add any articles you think might be helpful to read before writing the article -->
- [Wikipedia: Triangle ](https://en.wikipedia.org/wiki/Triangle )
- [More Examples ](https://mathbits.com/MathBits/TISection/Trig/AreaTrigTri.htm )