# Area of a Triangle SAS Calculator

Our area of a triangle SAS calculator can determine a triangle's area from any of its two sides and the corresponding inscribed angle. Note that **the abbreviation SAS stands for Side-Angle-Side.**

In this article, we shall briefly discuss the following:

- How to find the area of a triangle given 2 sides and an angle.
- What is a triangle's SAS area formula.
- Some FAQs.

## SAS area formula of a triangle

You might be familiar with the formula of a triangle's area given its **base** and **height**:

In the triangle above, we know only its **two sides**, $a$ and $b$, and the **angle** $\gamma$ between them. If we consider the side $b$ as the triangle's **base**, using trigonometry, we obtain its **height** as:

Therefore, the **SAS area formula** for a triangle is given by:

We can use this formula to calculate the triangle area with 2 sides and an angle.

## How do you find a triangle's area given two sides and an angle?

To find the **area** of a **triangle** given its **two sides** `a`

and `b`

, and the **inscribed angle** `γ`

, follow these simple steps:

**Multiply**the lengths of the**two sides**together to get`a × b`

.**Multiply**this value with the**sine**of the**angle**`γ`

, to get`a × b × sin(γ)`

.**Divide**this value by**half**to get the triangle**area**as`A = (a × b × sin(γ))/2`

.- Verify using our area of a triangle SAS calculator.

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## How to use this area of a triangle SAS calculator

Our calculator for the area of a triangle given 2 sides and an angle is simple and easy to use:

**Enter**the two sides you know.**Provide**the value of the inscribed angle. The calculator will automatically find the area.

And just like that, you can find the triangle area with 2 sides and an angle. Note that this area of a triangle SAS calculator can also work backward! Play around with it providing different inputs in any order, and enjoy the results!

## FAQ

### How do you find the missing side of a triangle from its two sides and angle?

The **formula** to calculate the **missing side** *c* of a triangle from its **two sides** *a* and *b* and the **inscribed angle** *γ* is:

*c = √(a ^{2} + b^{2} - 2abcos(γ))*

### What is the triangle area with two sides 3 and 4 which subtend 90°?

** 6 units**. To find this answer yourself, follow these steps:

**Multiply**the lengths of the**two sides**together to get`3 × 4 = 12`

.**Multiply**this value with the**sine**of the**angle**`90°`

, to get`12 × sin(90°) = 12 × 1 = 12`

.**Divide**this value by**half**to get the triangle**area**as`A = 12/2 = 6`

.- Verify using our area of a triangle SAS calculator.