How to Calculate the Area of a Right Triangle
The area of a right triangle is one of the simplest area calculations in geometry. Since the two legs of a right triangle are perpendicular to each other, one leg serves as the base and the other as the height. The formula is simply half the product of the two legs.
Area Formulas
From Two Legs
The most direct formula using both legs.
From Hypotenuse and Leg
Find the other leg first, then calculate area.
From Hypotenuse and Altitude
Using the altitude to the hypotenuse.
Understanding the Formula
The area formula A = (1/2) x a x b comes from the general triangle area formula A = (1/2) x base x height. In a right triangle, the two legs are perpendicular, so one naturally serves as the base and the other as the height. This makes right triangles the easiest type of triangle for area calculations.
Altitude to the Hypotenuse
The altitude from the right angle to the hypotenuse creates two smaller triangles that are similar to each other and to the original triangle. The length of this altitude is h = (a x b) / c. Since the area can also be expressed as A = (1/2) x c x h, we get two equivalent formulas.
Practical Examples
- A right triangle with legs 3 and 4: Area = (1/2)(3)(4) = 6 square units.
- A right triangle with legs 5 and 12: Area = (1/2)(5)(12) = 30 square units.
- A right triangle with hypotenuse 10 and leg 6: other leg = 8, Area = (1/2)(6)(8) = 24 square units.
- An isosceles right triangle with legs 7: Area = (1/2)(7)(7) = 24.5 square units.