Area of a Triangle SAS Calculator

Created by Krishna Nelaturu
Reviewed by Aleksandra Zając, MD
Last updated: Jun 05, 2023


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:

Area=12×base×height\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}
A triangle whose two sides and inscribed angle are known.
A triangle whose two sides and the inscribed angle are known.

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

h=asin(γ)h = a \cdot \sin(\gamma)

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

Area=12×a×b×sin(γ)\text{Area} = \frac{1}{2} \times a × b ×\sin(\gamma)

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:

  1. Multiply the lengths of the two sides together to get a × b.
  2. Multiply this value with the sine of the angle γ, to get a × b × sin(γ).
  3. Divide this value by half to get the triangle area as A = (a × b × sin(γ))/2.
  4. Verify using our area of a triangle SAS calculator.

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:

  1. Enter the two sides you know.
  2. 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 = √(a2 + b2 - 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:

  1. Multiply the lengths of the two sides together to get 3 × 4 = 12.
  2. Multiply this value with the sine of the angle 90°, to get 12 × sin(90°) = 12 × 1 = 12.
  3. Divide this value by half to get the triangle area as A = 12/2 = 6.
  4. Verify using our area of a triangle SAS calculator.
Krishna Nelaturu
Area of triangle from Side-Angle-Side (SAS)
Triangle area: triangle with two sides and angle between them (SAS)





Side a
cm
Side b
cm
Angle γ
deg
Area
cm²
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