1. Using Trigonometry to find area of a triangle The area of a triangle is one half the product of the lengths of two sides and sine of the included angle. Area of ABC = ½ bc(sin A) B C a c b A

2. c b a a C B A Substituting for h in (1) - - - - - (1) In Draw the perpendicular, h, from C to BA. Area of a Triangle ABC is a non-right angled triangle.

3. Any side can be used as the base, so Area of a Triangle The formula always uses 2 sides and the angle formed by those sides Area = = =

4. Any side can be used as the base, so Area of a Triangle The formula always uses 2 sides and the angle formed by those sides c b a a C B A Area = = =

5. Any side can be used as the base, so Area of a Triangle The formula always uses 2 sides and the angle formed by those sides c b a a C B A Area = = =

6. Any side can be used as the base, so Area of a Triangle The formula always uses 2 sides and the angle formed by those sides c b a a C B A Area = = =

7. 1.Find the area of the triangle PQR. Example 7 cm 8 cm R Q P Solution: We must use the angle formed by the 2 sides with the given lengths.

8. 1.Find the area of the triangle PQR. Example 7 cm 8 cm R Q P Solution: We must use the angle formed by the 2 sides with the given lengths. We know PQ and RQ so use angle Q

9. 1.Find the area of the triangle PQR. Example 7 cm 8 cm R Q P Solution: We must use the angle formed by the 2 sides with the given lengths. We know PQ and RQ so use angle Q cm 2 (3 s.f.)