Area of any triangle

You can find the area of any triangle if you are able to find two sides and the angle between the two sides.

The area of a triangle is equal to 1/2 times the base (or side 1), times the height (or side 2), times the sin of the angle between. Or, A=1/2(b)(h)(sin[angle])

If it is a right triangle, you can simplify it to A=1/2(b)(h) because sin(90) equals one.

Ex.1
Find the area of (in centimeters):

I drew a little dotted line where you should cut the figure so you can find the area. You don't want to cut it horizontally because that would destroy your right angle.

The area of the triangle on the right is going to be a little more difficult to find than the left. You have to find the angle of the left triangle to subtract to find the right.
We can use SOHCAHTOA, so the little part of 108 = sin^-1(5/13) = 22.620. Now we can subtract that from 108 to find the right side of 108.
108 - 22.620 = 85.38
Now we can use the formula to find the area of the triangle on the right.

The area of the triangle on the right = 1/2(13)(18)(sin85.38) = 116.620 cm^2.

The left triangle is a right triangle, and you can also see that it is a Pythagorean triple. The missing side and dotted line is 13.

The area of the left triangle = 1/2(5)(12) = 30 cm^2.

Now you add them together 116.620 + 30 = 146.620 cm^2.