More triangles

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

It is simply:

                                            Area = ½ ´ AC ´ BC ´ sin C

Or:

                                            Area =  ½ ´ AB ´ AC ´ sin A

Or:

                                            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:

Solution

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.

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’.