More triangles

Finding the Area of a Triangle

There is a simple formula for finding the area of a triangle (any triangle, does not have to be right angled).

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It is simply:

                                            Area = ½ ´ AC ´ BC ´ sin C


                                            Area =  ½ ´ AB ´ AC ´ sin A


                                            Area = ½ ´ BA ´ CB ´ sin B

To use the formula, you must know two side lengths and the angle between those sides.

Triangle area question

Find the area of the following triangle:


                                            Area = ½ ´ AC ´ BC ´ sin C

Let’s make AC the side of length 6, BC the side of length 7, and 110° the angle C.

Then the area is:

                                                    ½ ´ 6 ´ 7 ´ sin 110º

                                                   = 19.73 square units.

Always check to see whether the answer makes approximate sense – looking at the triangle, 19.73 seems like a reasonable answer for its area.

Handy Hint #1 -  Units

Whenever you have to give an area, make sure that you put units at the end.  They could be cm2, mm2, m2, km2 or if no units are given, put ‘square units’.