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Well, based from what I learned, the area of a triangles is found out using the formula:
              Base x Height x 1/2 

1.) The base of a triangle is 5 and its height is 4. What is the area of the triangle?
 Formula:  B x H x 1/2
  =5 x 4 x 1/2
=20 x 1/2
=10 squared units
Note: The one that is placed is "squared units" because there is no unit given in the problem.

2.) The base of a triangle is 5 cm and its height is 4 cm. What is the area of the triangle?
Formula: B x H x 1/2
          =  5 cm x 4 cm x 1/2
         = 20  cm^{2} x 1/2
          =   \frac{2o cm squared}{10}
          = 10  cm^{2}
Note: Never forget the units! If you forget the unit, the rest is a mistake! Never forget it! The unit of area is squared unit/s!

or using sine function when you are given one angle and the length of the two adjacent sides. A=1/2*bc*sinA where A is the angle and b and c are the length of the sides adjacent to the angle. Or using Heron's formula where area is given as, A= sqrt[s(s-a)(s-b)(s-c)] where 's' is the semi-perimeter of the triangle or the perimeter divided by 2 and a,b,&c are the lengths of the sides of the triangle.
Area Of A Triangle = Base x Height x 1/2 (or divide by 2)