How to find a triangle's area
The area of a triangle is half the base times the perpendicular height: area = ½ × base × height. For a base of 10 and height of 6: ½ × 10 × 6 = 30 square units. The height must be measured perpendicular to the chosen base. Adding the three sides rather than combining base and height gives the perimeter instead.
How to use this calculator
Enter the base and the perpendicular height. The result is the area in square units. For a right triangle from its two legs, the right triangle calculator finds the area too.
- Height must be perpendicular to the base, not the length of a sloping side.
- In a right triangle the two legs serve as base and height directly, so ½ × 3 × 4 = 6.
- For obtuse triangles the height may fall outside the triangle — extend the base line to measure it.
Choosing a base and other methods
Any of the three sides can act as the base, and each pairs with its own perpendicular height. All three combinations give the same area, which makes for a handy check: if two choices disagree, one height was measured wrongly. Pick whichever side has the height you can actually measure.
When no height is available, other routes exist. Heron's formula works from three sides alone, the sine rule ½ab·sin(C) works from two sides and the angle between them, and coordinate geometry gives the area straight from three vertices. All of them reduce to ½ × base × height once the missing perpendicular is known. Two identical triangles joined along their longest side make a parallelogram, which is why the parallelogram area calculator drops the halving step.
Frequently asked questions
- What is the formula for the area of a triangle?
- Area = ½ × base × height, where the height is measured perpendicular to the base.
- What is the area of a triangle with base 10 and height 6?
- 30 square units (½ × 10 × 6).
- How do I find the area from three sides?
- Use Heron's formula: with s = (a+b+c)/2, area = √(s(s−a)(s−b)(s−c)).
- Does the base have to be the bottom side?
- No. Any side can be the base, as long as you use the height perpendicular to that side.
- What if I only know the slanted side, not the perpendicular height?
- Do not use the slanted side as the height — it is longer and will overstate the area. Either drop a perpendicular and measure it, or use two sides with the angle between them: area = ½ × a × b × sin(C).