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| Area of a Triangle |
Area of a Triangle
A triangle is a three sided, two dimensional polygon. There are two methods to determine the area.
Method 1
The area of a triangle can be calculated by multiplying 0.5 to the base length to the perpendicular height.
Mathematically this is expressed as:
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.
Mathematically this is expressed as:
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.
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
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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 units2
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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 units2