Find the area of a triangle.
Half the product of the base and the perpendicular height.
Area: ½ × base × height
The triangle area calculator uses the classic rule: area equals half the base times the perpendicular height. You enter the length of any side as the base and the height measured straight up from that side to the opposite corner, and it returns the area in square units.
This is the first area formula for triangles taught in Indian schools, from Class 6 onwards, and it shows up in land measurement, construction drawings, roof and gable calculations, and design work. A triangular plot corner, a sloping gable wall to be painted or a sail cut from cloth can all be handled with it, provided you know or can measure the height. When you only know the three sides, a different method called Heron's formula is used instead, and the triangle calculator on this site handles that.
1. Choose any side of the triangle as the base and measure its length.
2. Find the perpendicular height: the straight-line distance from the base, or its extension, to the opposite vertex, meeting the base at 90°.
3. Make sure the base and height are in the same unit.
4. Multiply base by height.
5. Divide by 2: Area = ½ × base × height.
6. State the answer in square units, such as cm² or m².
Take a triangle and a copy of it rotated by 180°. Place them together along one side and you always get a parallelogram with the same base and height. A parallelogram's area is base × height, because you can slice off a triangle from one end and move it to the other to form a rectangle. The triangle is exactly half of this shape, so its area is ½ × base × height. The argument works for acute, right and obtuse triangles.
A triangle has three possible bases, each with its own height. The products base × height are equal for all three, so the area does not depend on the choice. For an obtuse triangle, the height from some bases falls outside the triangle, and you must extend the base line to meet it. For a right triangle, the two sides forming the right angle are already a base and height pair, so the area is simply half their product.
If you know two sides and the angle between them, the area is ½ab sin C, which follows because b sin C is the height on side a. If you know only the three sides, Heron's formula works without any height. In coordinate geometry, the area of a triangle with vertices (x₁, y₁), (x₂, y₂), (x₃, y₃) is ½|x₁(y₂ − y₃) + x₂(y₃ − y₁) + x₃(y₁ − y₂)|. All of these give the same answer as ½ × base × height.
Lakshmi is painting the triangular gable wall of her village house, which is 7.5 metres wide at the bottom and rises 3.2 metres to the peak.
Answer: Area 12
Using the slanting side as the height. The height must be perpendicular to the base.
Forgetting to halve, which gives the area of the whole parallelogram instead of the triangle.
Pairing a height with the wrong base. Each height belongs to the side it is perpendicular to.
Mixing units, such as a base in metres and a height in centimetres, which gives a nonsense area.
Reporting the answer in linear units instead of square units.
Estimating paint or cladding for gable ends and triangular walls.
Measuring triangular land parcels, often by splitting an irregular plot into triangles.
Cutting fabric, glass or sheet metal into triangular panels.
Solving mensuration problems in Class 6 to 10 textbooks and competitive exams.
Computing roof truss areas and sail areas in design work.
What if I only know the three side lengths, not the height?
You would need to use Heron's formula instead. It works out the area directly from the three sides, without needing the height.