Area of a Right Triangle Calculator
If you are wondering how to find right triangle area, you're in the right place - this area of a right triangle calculator is a tool for you. Whether you're looking for the equation given triangle legs, leg and hypotenuse or side and angle, you won't be disappointed - this calculator has all of them implemented. Scroll down to find out more about area of right triangle formulas or simply give our calculator a try!
Area of right triangle formulas
The basic equation is a transformed version of a standard triangle height formula (
a * h / 2). Because the right triangle legs are perpendicular to each other, one leg is taken as a base and the other is a right triangle height:
area = a * b / 2
Sometimes it's not so obvious - you have other values given, not two legs. Then what?
If you have one leg and hypotenuse given, use the Pythagorean theorem to find the missing leg:
a² + b² = c²
Then take a square root of the transformed equation:
cwe find that
b = √(c² - a²):
area = a * √(c² - a²) / 2
cwe calculate that
a = √(c² - b²):
area = b * √(c² - b²) / 2
If you know one angle and hypotenuse, you can use the law of sines:
a = c * sin(α)
b = c * sin(β) = c * sin(90-α) = c * cos(α)
area = c² * sin(α) * cos(α) / 2
Given one angle and one leg, find the area using e.g. trigonometric functions:
a/b = tan(α)and
b/a = tan(β)
area = b * tan(α) * b / 2 = b² * tan(α) / 2
area = a * a * tan(β) / 2 = a² * tan(β) / 2
If you've just noticed that your triangle is not a right triangle, check out this general triangle area tool.
Area of an isosceles right triangle
Isosceles right triangle is a special right triangle, sometimes called a 45-45-90 triangle. In such triangle the legs are equal in length (as a hypotenuse always must be the longest of the right triangle sides):
a = b
One leg is a base and the other is the height - there is a right angle between them. So the area of an isosceles right triangle is:
area = a² / 2
How to use the area of a right triangle calculator
Let's show the step by step calculation:
- Pick one option, depending on what you have given. Assume that we know one leg and angle, so we change the selection to given angle and one side.
- Enter the values. For example, we know that α = 40° and b is 17 in.
- Watch our area of a right triangle calculator performing all calculations for you! The area of the chosen triangle is 121.25 in².