54 lines
2.0 KiB
Markdown
54 lines
2.0 KiB
Markdown
---
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title: Area of a Triangle
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---
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<!-- The article goes here, in GitHub-flavored Markdown. Feel free to add YouTube videos, images, and CodePen/JSBin embeds -->
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## Area of a Triangle
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A triangle is a three sided, two dimensional polygon. There are two methods to determine the area.
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### Method 1
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The area of a triangle can be calculated by multiplying 0.5 to the base length to the perpendicular height.
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Mathematically this is expressed as:
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### Method 2
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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.
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Mathematically this is expressed as:
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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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### Terminology
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Base - The bottom side. Select a side that is known.
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Perpendicular Height - The height of the triangle, measured perpendicular to the base, to the tallest point of the triangle.
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Sin - The sine trigonometric expression.
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### Examples
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1. Find the area of a triangle with a base length of 4 units and a perpendicular height of 12 units
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Area = 0.5 x 4 x 12 = 24 units<sup>2</sup>
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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?
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Area = 0.5 x 3 x 6 x sin(30 degrees) = 4.5 units<sup>2</sup>
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#### More Information:
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<!-- Please add any articles you think might be helpful to read before writing the article -->
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- [Wikipedia: Triangle](https://en.wikipedia.org/wiki/Triangle)
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- [More Examples](https://mathbits.com/MathBits/TISection/Trig/AreaTrigTri.htm)
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