20.8 The area of any triangle — Practise

Work independently. Estimate where useful, show your method, and check units. In the mixed questions, choose the method and give a reason.

1. H Find the area of a triangle with sides 8 cm and 5 cm and included angle 30°.
2. H Find the area when sides 6 cm and 10 cm include an angle of 90°.
3. H Find the area when sides 7 cm and 9 cm include an angle of 40°, to 1 decimal place.
4. H Two sides are 12 cm and 8 cm, with included angle 60°. Find the area exactly.
5. H A triangle has sides 5 cm and 11 cm with included angle 120°. Find its area.
6. H Find the area for sides 9 cm and 10 cm with included angle 25°, to 1 decimal place.
7. H A triangle has sides 13 cm and 17 cm and included angle 35°. Find the area to 1 decimal place.
8. H The area is 20 cm². Two sides are 8 cm and 10 cm. Find the included angle, taking the acute solution.
9. H The area is 20 cm^2. One side is 10 cm and the included angle is 30°. Find the other side.
10. H A triangle has sides 8 cm and 11 cm with an included angle of 60°. Which method finds its area: the area formula $\frac12 ab\sin C$, the sine rule, or the cosine rule? Give a reason, then find the area exactly.