Area with Sine

Half a b sine C

An interactive lesson with 6 steps, about 5 minutes: you predict, drag and solve, with instant feedback on every answer. It runs in your browser and needs JavaScript.

What you’ll learn

• Area $= \tfrac12 ab\sin C$, using two sides and the angle between them.
• $\sin C = \sin(180° - C)$, so an angle and its supplement give the same area.
• Polygons in a unit circle have areas approaching $\pi$.

Steps

1. Height from an angle
2. At 30°
3. The same area again
4. A field
5. Squeezing π
6. Twelve sides