Trigonometry: Area of a Triangle
This is a free lesson from our course in Trigonometry
 
   
This lesson introduces and walks you through the basic concepts of how to determine the area of a triangle. You'll learn it with the help of some examples, practice questions with solution and presenting video explanation by the instructor that brings in an element of real-class room experience. There are several ways to compute the area of a triangle E.g. the basic formula is area of a triangle is half the base times the height. For example: In a right triangle, with base (b) and the height (h) perpendicular to base, the area of triangle is
         Area = 1/2 x base x height = 1/2 x b x h
(More text below video...)
<h2> Trigonometry-Area of a Triangle</h2> <p> area of a triangle, triangle, base, height, example, solution, video, acute triangle, right triangle, sides, angle, SSS, Heronís Formula, trigonometry help, semi perimeter, semiperimeter, Heronís Formula, practice questions, quizzes</p> <p> In a right triangle, with base (b) and the height (h) perpendicular to base, the area of triangle is 1/2 x base x height In cases of non right triangle ABC in which the height is unknown, the area of a triangle is given by the formula Area = A = 1/2 bc sin A = 1/2 ac sin B = 1/2 ab sin C</p>
Other useful lessons:
Law of Sines & Cosines
Area of a Triangle
Using law of Sines and Cosine Formulas

(Continued from above) In cases of non right triangle ABC in which the height is unknown, the area of a triangle is given by the formula

         Area = A = 1/2 bc sin A
                      = 1/2 ac sin B
                      = 1/2 ab sin C

So the area of triangle is obtained by multiplying one-half times the product of any two sides and the sine of the included angle.
Take an example of a triangle ABC, where a = 5, b = 6 and mC = 60, i.e. we have two sides and the included angle. You may use from above formulas, the one that has sin C, i.e., A = 1/2 ab sin C and that yields A = 153/2 square units.
In other cases, when three sides of a triangle are given (SSS), its area 'A' is calculated using the Heron's Formula:
          Area = A = s(s - a)(s - b)(s - c)
Where a, b and c are the lengths of the sides of a triangle and s = (a + b + c)/2 is the semi perimeter. 

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