Triangle Area Calculator – Find Area from Base and Height
Calculate the area of any triangle instantly. Enter the base and height to get the area using the standard formula – no sign-up required.
Enter the base length
The base can be any side of the triangle. Enter its length in your preferred unit (cm, m, inches, etc.).
Enter the height
The height is the perpendicular distance from the base to the opposite vertex. It must be at a 90-degree angle to the base.
Get your result
Click Calculate to see the area. The result is in square units matching your input (square cm, square meters, etc.).
The area of a triangle equals half the base times the height: A = ½ × b × h. This formula works for all triangles – right, acute, obtuse, scalene, isosceles, or equilateral.
Why divide by 2? Picture a rectangle with the same base and height as your triangle. That rectangle's area is b × h. Now draw a diagonal – you've split it into two identical triangles. Each triangle is exactly half the rectangle's area.
The height must be perpendicular to the base. In a right triangle, one leg serves as the height when the other leg is the base. In other triangles, you may need to draw an altitude line from the vertex straight down to the base.
| Method | Formula | When to Use |
|---|---|---|
| Base and Height | A = ½bh | When you know base and perpendicular height |
| Heron's Formula | A = √[s(s-a)(s-b)(s-c)] | When you know all three sides (s = semi-perimeter) |
| Two Sides and Angle | A = ½ab sin(C) | When you know two sides and the included angle |
| Equilateral Triangle | A = (√3/4) × s² | When all three sides are equal |
| Coordinates | A = ½|x₁(y₂-y₃) + x₂(y₃-y₁) + x₃(y₁-y₂)| | When you have vertex coordinates on a grid |
By Side Lengths
- Equilateral: All three sides equal, all angles 60°. Area = (√3/4) × side²
- Isosceles: Two sides equal, two angles equal. Height splits base in half.
- Scalene: All sides different, all angles different. Use base-height or Heron's formula.
By Angles
- Right Triangle: One 90° angle. The two legs can serve as base and height.
- Acute Triangle: All angles less than 90°. Height falls inside the triangle.
- Obtuse Triangle: One angle greater than 90°. Height may fall outside the triangle.
| Application | Example | Calculation |
|---|---|---|
| Roofing | Gable end of house | Base = 30 ft, Height = 12 ft → Area = 180 sq ft |
| Land Surveying | Triangular plot of land | Use Heron's formula with measured sides |
| Sailing | Sail area calculation | Base = boom length, Height = mast height |
| Construction | Triangular support beam | Calculate cross-sectional area for load analysis |
| Art and Design | Triangular canvas or frame | Determine material needed for coverage |
What is the formula for triangle area?
The basic formula is Area = ½ × base × height. The base can be any side, and the height is the perpendicular distance from that base to the opposite vertex. This formula works for all triangle types.
How do I find the height of a triangle?
In a right triangle, one leg is the height when the other leg is the base. For other triangles, draw a line from the vertex perpendicular to the base (or its extension). If you know the area and base, rearrange the formula: height = 2 × area ÷ base.
Can I calculate area without the height?
Yes. If you know all three sides, use Heron's formula. If you know two sides and the angle between them, use A = ½ab sin(C). For equilateral triangles, use A = (√3/4) × side².
Why is triangle area half of base times height?
A triangle is exactly half of a parallelogram with the same base and height. Two identical triangles can always be arranged to form a parallelogram. Since parallelogram area is base × height, triangle area is half that.
What units should I use?
Use any consistent units for base and height. The area will be in square units – if you measure in centimeters, area is in square centimeters. If you measure in feet, area is in square feet.
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