--- title: 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. ![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. ### 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 units² 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 units² #### More Information: - [Wikipedia: Triangle](https://en.wikipedia.org/wiki/Triangle) - [More Examples](https://mathbits.com/MathBits/TISection/Trig/AreaTrigTri.htm)