Triangle area without a height: use the three sides
Three valid side lengths determine a triangle’s area. Heron’s formula avoids measuring a perpendicular height that may be difficult to reach.
Triangle calculator →Check that a triangle exists
Use positive side lengths in the same unit. The sum of any two must be strictly greater than the third. Sides 4, 5 and 6 pass this test; sides 2, 3 and 5 only form a straight line and are rejected. A sketch is helpful but does not replace checking the numbers, especially when measurements were copied from different drawings.
Work through Heron’s formula
For sides 4, 5 and 6, the semiperimeter s is (4+5+6)/2 = 7.5. Area is √[7.5×3.5×2.5×1.5] = √98.4375, approximately 9.92157 square units. The perimeter is 15 units. Enter the three sides in the triangle calculator to obtain both quantities; swapping the order of the sides does not change either answer.
Know what the answer represents
This tool handles a flat triangle from three sides; it does not infer missing sides or angles from incomplete information. The formula assumes straight boundaries. For an irregular plot, divide the outline into measured triangles or obtain a suitable survey instead of entering three convenient-looking distances. Retain extra digits until the final rounding, but do not imply survey precision beyond the accuracy of your measurements. The perimeter uses the original length unit, not the squared unit displayed beside the area result.
Try the calculators
- Triangle calculator
Calculate area and perimeter from three sides.
- Rectangle area
Calculate a rectangle’s area and perimeter.
- Scientific calculator
Arithmetic, powers, trigonometry and logarithms.