# Area of a triangle = 0.5absinx - using the two side lengths and the angle between them.

The alternative method to calculating the area of a triangle (instead of 1/2bh) is by using the formula:

Area of triangle = ½absinx

a and b are the two side lengths of the triangle and x is the angle between the two sides.

This formula can be used in all types of triangles, but make sure you have 2 side lengths and the angle between them. This formula is useful when working out the area of the segment and in situations when the perpendicular height of the triangle is not given

**Example 1**

The diagram shows triangle ABC. AB is 7cm and AC is 12cm. Angle BAC is 21⁰. Work out the area of the triangle giving your answer to 1 decimal place.

Here you are given two side lengths and the angle between these two sides so you can use the formula Area of triangle = ½absinx.

So a = 7cm and b = 12cm (It doesn’t matter if you do a=12 and b = 7) and angle x = 21. All you need to do now is substitute these numbers into the formula for the area of a triangle:

Area of triangle = ½absinx

Area of triangle = ½ × 7 × 12 × sin(21)

Area of triangle = 15.1 centimetres squared rounded to 1 decimal place.

So the formula gives an answer of 15.1 cm²

**Example 2**

The diagram shows triangle DEF. DE is 14 m, EF is 11 m and DF is 15.4 m. Angle DEF is 75⁰. Work out the area of the triangle giving your answer to 1 decimal place.

On this example you need to be careful which side lengths to use. Make sure you choose the side lengths either side of the given angle.

Therefore you have; a = 14 m and b = 11m (again it doesn’t matter which one is a and which one is b) and angle x = 75⁰. The other length of 15.4m is not needed to work out the area of the triangle - it is only there to catch you out. All you need to do now is substitute these numbers into the formula for the area of a triangle:

Area of triangle = ½absinx

Area of triangle = ½ × 14 × 11 × sin(75)

Area of triangle = 74.4 m² (rounded to 1 decimal place).

So the formula gives an answer of 74.4 cm² for the area of the triangle.

As you can see using the formula ½absinx for working out the area of a triangle is not as difficult as it looks as long as you have a scientific calculator. Just remember to use the two sides and the angle between.

## More by this Author

- 26
A compound shape is a shape that is made up from other simple shapes. In this article we will be working out the area of a L shape (made up from 2 rectangles). To find the area of a compound shape, follow these simple...

- 0
The density, mass and volume triangle is as follows: So if you wanted to work out the density, you would cover up density in the magic triangle to give: Density = Mass/Volume (since mass is above volume) So if...

- 0
The surface area of a triangular prism can be found in the same way as any other type of prism. All you need to do is calculate the total area of all of the faces. A triangular prism has 5 faces, 3 being rectangular and...