Triangle Area Calculator
Calculate the area of a triangle using three different methods: base and height, three sides (Heron's formula), or two sides and the included angle (SAS). Perfect for students, teachers, engineers, and anyone working with geometry.
What Is a Triangle?
A triangle is a three-sided polygon with three angles that always sum to 180°. Triangles are the simplest polygon and are fundamental to geometry, trigonometry, and many real-world applications — from construction and engineering to art and design.
The area of a triangle is the amount of space enclosed within its three sides. This calculator supports three methods for calculating triangle area:
- Base & Height: A = ½ × base × height — the simplest method when you know the base and perpendicular height.
- Heron's Formula: A = √(s(s-a)(s-b)(s-c)) where s = (a+b+c)/2 — works when you know all three side lengths.
- SAS (Side-Angle-Side): A = ½ × a × b × sin(C) — works when you know two sides and the included angle.
How Does the Triangle Area Calculator Work?
The calculator uses standard geometric formulas for each method:
Base & Height Method:
Area = ½ × base × height
Example: base = 10, height = 8 → Area = ½ × 10 × 8 = 40
Heron's Formula:
s = (a + b + c) / 2
Area = √(s(s-a)(s-b)(s-c))
Example: a=10, b=12, c=14 → s=18, Area = √(18×8×6×4) ≈ 58.79
SAS Method:
Area = ½ × a × b × sin(C)
Example: a=10, b=12, C=45° → Area = ½ × 10 × 12 × sin(45°) ≈ 42.43
Simply choose your method, enter the required dimensions, and the calculator will instantly compute the area, perimeter, and display the formula used.
Why Use This Triangle Area Calculator?
- Three Methods: Choose from base & height, Heron's formula, or SAS.
- Unit Flexibility: Switch between metric and imperial units.
- Visual Breakdown: A chart shows the triangle's dimensions.
- Educational: See the formula and step-by-step calculation.
- Free & Private: No registration, no data storage.
Types of Triangles
- Equilateral: All three sides equal, all angles 60°.
- Isosceles: Two sides equal, two angles equal.
- Scalene: All sides different.
- Right Triangle: One angle is 90°.
- Acute Triangle: All angles less than 90°.
- Obtuse Triangle: One angle greater than 90°.
❓ Triangle Area Calculator FAQ
How do I calculate the area of a triangle?
There are three common methods: 1) Base × Height ÷ 2, 2) Heron's formula for three sides, and 3) ½ × side a × side b × sin(angle C) for SAS. This calculator supports all three methods.
What is the formula for the area of a triangle?
The most common formula is A = ½ × b × h, where b is the base and h is the perpendicular height. Heron's formula is A = √(s(s-a)(s-b)(s-c)) where s is the semi-perimeter.
What is Heron's formula?
Heron's formula calculates the area of a triangle when you know all three side lengths. It is A = √(s(s-a)(s-b)(s-c)), where s = (a+b+c)/2 is the semi-perimeter.
What is the SAS method for triangle area?
The SAS (Side-Angle-Side) method uses two sides and the included angle: A = ½ × a × b × sin(C), where a and b are the sides and C is the angle between them.
What is the difference between base and height vs. Heron's formula?
Base and height require you to know the perpendicular height of the triangle. Heron's formula only requires the three side lengths — it's useful when you don't have the height.
How do I find the height of a triangle?
The height is the perpendicular distance from a vertex to the opposite side (the base). You can calculate it using trigonometry or by using Heron's formula to find the area and then working backward: height = 2 × Area ÷ base.
What is the perimeter of a triangle?
The perimeter is the sum of all three sides: P = a + b + c. This calculator shows the perimeter for all methods.
How do I calculate the area of a right triangle?
For a right triangle, the area is ½ × leg1 × leg2 (the two sides that form the right angle). This is the same as base × height ÷ 2.
How do I calculate the area of an equilateral triangle?
For an equilateral triangle with side length s, the area is A = (√3/4) × s². You can also use Heron's formula with a = b = c = s.
What is the semi-perimeter of a triangle?
The semi-perimeter is half the perimeter: s = (a + b + c) / 2. It's used in Heron's formula to calculate the area.
How do I convert triangle area to acres?
1 acre = 43,560 square feet. If your area is in square feet, divide by 43,560 to get acres. This calculator can display area in acres for large triangles.
Can I use this calculator for any triangle?
Yes, this calculator works for all triangles — equilateral, isosceles, scalene, right, acute, and obtuse. Just choose the appropriate method for your known measurements.
What units does this calculator support?
The calculator supports metric (centimeters, meters) and imperial (inches, feet) units. You can switch between them using the unit system selector.
What is the area of a triangle with sides 3, 4, and 5?
Using Heron's formula: s = 6, Area = √(6×3×2×1) = √36 = 6 square units. This is a right triangle with legs 3 and 4.
What is the area of a triangle with base 10 and height 5?
Area = ½ × 10 × 5 = 25 square units.
What is the area of a triangle with sides 5, 6, and 7?
Using Heron's formula: s = 9, Area = √(9×4×3×2) = √216 ≈ 14.70 square units.
What is the area of a triangle with two sides 8 and 10 and included angle 60°?
Area = ½ × 8 × 10 × sin(60°) = 40 × 0.866 = 34.64 square units.
How accurate is this triangle area calculator?
This calculator provides accurate results based on standard geometric formulas and the values you enter. The precision can be adjusted up to 5 decimal places.