The Triangle Surface Area Calculator calculates the area of a triangle using whichever measurements you have: base and height (A = ½ × b × h), all three sides (Heron’s formula), or two sides and the angle between them (A = ½ × a × b × sin C).
Triangle Surface Area Calculator
Area of a triangle from base and height, three sides (Heron), or two sides and the included angle.
A flat triangle has area rather than surface area, which is what this calculator returns. For a 3D solid with triangular faces, use the triangular prism or triangular pyramid calculator. Enter your values below.
Formula
Base and height: A = (b × h) ÷ 2
Three sides (Heron’s formula): A = √(p(p − a)(p − b)(p − c)), where p = (a + b + c) ÷ 2
Two sides and included angle: A = ½ × a × b × sin C
Where:
- A = area
- b = base; h = perpendicular height to that base
- a, b, c = side lengths; p = semi-perimeter
- C = the angle between sides a and b
How the Calculation Works
Step 1: Pick the formula that matches your measurements.
Step 2: For Heron’s formula, first find the semi-perimeter p, then multiply p by (p − a), (p − b) and (p − c).
Step 3: Take the square root (Heron) or halve the product (base × height, or a × b × sin C). The result is in square units.
Variables Explained
| Variable | Meaning | Unit |
|---|---|---|
| b, h | Base and perpendicular height | cm, m, in, ft |
| a, b, c | Side lengths | cm, m, in, ft |
| C | Included angle | degrees or radians |
| A | Area | cm², m², in², ft² |
Example Calculation
Base and height
Given: base = 8 cm, height = 5 cm
Result: A = 8 × 5 ÷ 2 = 20 cm²
Three sides
Given: a = 5 cm, b = 6 cm, c = 7 cm
p = (5 + 6 + 7) ÷ 2 = 9
Calculation: A = √(9 × 4 × 3 × 2) = √216
Result: A ≈ 14.70 cm² (perimeter 18 cm)
Two sides and an angle
Given: a = 5 cm, b = 6 cm, C = 60°
Calculation: A = 0.5 × 5 × 6 × sin 60° = 15 × 0.8660
Result: A ≈ 12.99 cm²
Common Area Conversion Table
| Unit | Equivalent |
|---|---|
| 1 m² | 10,000 cm² |
| 1 ft² | 144 in² |
| 1 m² | 10.7639 ft² |
Shape Properties
A triangle’s angles always add up to 180°, and any two sides together must be longer than the third. The calculator checks this and warns you if three sides cannot form a triangle.
Special triangles
- Right triangle: the two legs are the base and height, so A = ½ × leg₁ × leg₂.
- Equilateral triangle: A = (√3 ÷ 4) × side².
Dimensions Explained
Height must be perpendicular
The height is measured at a right angle from the base to the opposite corner, not along a sloping side. If you only have the sides, use the three-sides mode.
Included angle
In the SAS mode the angle must be the one between the two sides you enter.
Frequently Asked Questions
How do you find the area of a triangle?
Multiply the base by the perpendicular height and divide by 2.
How do you find the area of a triangle with three sides?
Use Heron’s formula: A = √(p(p − a)(p − b)(p − c)), with p half the perimeter.
How do you find the area of a triangle without the height?
Use Heron’s formula (three sides) or ½ × a × b × sin C (two sides and the angle between them).
Does a triangle have surface area?
A flat triangle has area. Surface area applies to 3D shapes such as triangular prisms and pyramids.
What is the surface area of a triangular prism?
A = 2 × triangle area + perimeter × prism length. Use the Triangular Prism Surface Area Calculator.
