How to calculate triangle area
Area = ½ × base × height. Use consistent length units; the result is in square units. For example, measurements in metres produce square metres (m²). Enter the measured dimensions, select the matching method and choose Calculate area.
Practical questions
How do I measure the area of a triangular garden?
If the base is 6 m and its perpendicular height is 4 m, the area is 12 m². Height is the shortest distance from the opposite corner to the line containing the base; it is not usually a sloping side.
What if I only know the three boundary lengths?
Select Three sides. For sides of 3 m, 4 m and 5 m, Heron’s formula gives an area of 6 m². The two shorter sides must add to more than the longest side.
Which angle should I enter with two sides?
Use the angle where the two measured sides meet, in degrees. Sides of 6 m and 4 m with an included angle of 30° give an area of 6 m². An angle opposite either side is not interchangeable with the included angle.
Why is perimeter unavailable in base-and-height mode?
Base and perpendicular height determine area, but they do not determine the other two side lengths. Different triangles can have the same base and height but different perimeters.
Can the height fall outside the triangle?
Yes. In an obtuse triangle, the perpendicular from a vertex may meet an extension of the base. The same base-times-height formula still applies.
How do I calculate the area of a triangular gable for painting?
Measure the horizontal base and the perpendicular rise to the peak. A triangular gable with an 8 m base and a 3 m rise has an area of 12 m². Subtract windows or other uncovered openings separately. This gives the triangular face area, not the area of the sloping roof.
Can I estimate fabric for a triangular flag or sail?
For a flat triangle with a 5 m base and a perpendicular height of 2.4 m, the geometric area is 6 m². Seams, hems, reinforcement and cutting layout require additional fabric. Curved edges or a shaped three-dimensional sail are not fully represented by a straight-sided triangle.
How can I divide a four-sided plot into triangles?
Draw a diagonal between opposite corners to split a simple four-sided plot into two triangles. Calculate both triangle areas and add them. For example, areas of 18 m² and 24 m² give a total of 42 m². Your measurements must describe the two triangles without gaps or overlaps.
Can I use a sloping side as the height?
Only when that side is perpendicular to the selected base. For example, a right triangle with perpendicular sides of 3 m and 4 m has an area of 6 m²; the 5 m sloping side is not the height for either of those bases. Use three-side mode if you know boundary lengths but not the perpendicular height.
What do I do if three measured sides are rejected?
Recheck the measurements and units. Sides of 2 m, 3 m and 6 m cannot close into a triangle because 2 + 3 is less than 6. If the two shorter sides add exactly to the longest, the shape is flat and has zero area. Small measurement errors matter particularly for nearly flat triangles.
Does this give the surface area of a sloping triangular panel?
Yes, if the dimensions describe the triangle in the plane of the panel. Measurements taken from a horizontal plan give its projected area instead. For a sloping panel, use its actual side lengths or a base and perpendicular height measured along the panel’s surface.