1. Area of triangle = 1/2absinC
Area of Triangles A B C a b
The area of a triangle can be found from two sides and the angle between them.
Area of triangle = 1/2absinC
Also
Area of triangle = 1/2acsinB
Area of triangle = 1/2bcsinA

2. Ex1 Ex2 A B C 4cm 2.5cm Area of triangle = 1/2absinC
70°
Area of triangle = 1/2absinC
= 0.5 X 4 X 2.5 x sin70°
= 4.7cm2
Ex2 K L M
30m
35m
130°
Area of triangle = 1/2kmsinL
= 0.5 X 30 X 35 x sin130°
= 402m2

3. Find the area of this parallelogram.
Ex3
Find the area of this parallelogram. P
Area  = 1/2pqsinR
22cm
= 0.5 X 11 X 22 X sin66°
= 110.5cm2
66° R Q
11cm
So area of parallelogram = 2 X 110.5
= 221cm2

4. Ex4 Find the area of this quadrilateral.
15cm
14cm
15cm
76.6°
76.6°
14cm
Area = 0.5 X 14 X 15 x sin76.6°
= 102cm2
20cm
21cm
52°
20cm
21cm
52°
Area = 0.5 X 20 X 21 x sin52°
Total area = 267cm2
= 165cm2

5. If A + B = 180 then sinA° = sinB°
Obtuse Angles
A B A+B sinA° sinB°
180
0.342
0.342
180
0.574
0.574
180
0.940
0.940
180
0.682
0.682
CONCLUSION
If A + B = 180 then sinA° = sinB°
Ex4
sinx° = 0.643
so x = sin
= 40°
or 140°