# Area of triangles: 1/2 a*b sin(C)

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##### Intros

##### Examples

###### Lessons

**Proof: Area of Triangle = $\frac{1}{2} ab\sin C$**Using the given diagram, prove that the area of a triangle can be found by the equation $\frac{1}{2} ab\sin C$

**Finding the Area of a Triangle Given 2 Sides and the Angle in Between**$\Delta XYZ$ has side lengths $XY$=9cm, $XZ$=12cm and $\angle YXZ$=42°. Find the area of $\Delta XYZ$. Give your answer to 1 decimal place.

**Area of Isosceles Triangles**The area of an isosceles triangle $\Delta ABC$ is 42.25 $cm^{2}$. If $\angle A$=30°, find the length of $AB$ in exact value.

**Area of Equilateral Triangles**An equilateral triangle has side length 4cm. Find its area and give your answer in exact value.

**Determining the Areas of Different Triangles**Find the area of the following triangle.

Find the area of the following right-angled triangle.