Triangle Area Calculator
Area of a triangle from its base and height.
Input sheet
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From a triangular garden bed to a roof gable to a sail, the area of a triangle comes up constantly. The classic base-and-height formula handles any triangle, not just right ones.
How it works
Area of a triangle is one half times base times height.
A triangle is exactly half of the rectangle that shares its base and height, which is where the one-half comes from. The height must be the perpendicular distance from the base to the opposite vertex — not the slanted edge.
This formula works for every triangle as long as you measure the height straight up from the base. For an obtuse triangle the foot of that height may land outside the base, but the math is unchanged.
Area = ½ × base × height
Worked examples
A triangle with a base of 10 and a height of 6. → 30 square units
½ × 10 × 6 = 30.
A triangular wall section, base 12 ft and height 9 ft. → 54 square feet
½ × 12 × 9 = 54 square feet.
Tips & gotchas
- Always use the perpendicular height, not the length of a sloped side — using the slant overstates the area.
- If you only know the three side lengths, use Heron's formula instead of base-and-height.
- Base and height must share the same unit; the result comes out in that unit squared.
FAQ
What if I don't know the height, only the three sides?
Use Heron's formula: compute the semi-perimeter s = (a + b + c) ÷ 2, then area = √(s(s−a)(s−b)(s−c)).
Does this work for right triangles?
Yes. In a right triangle the two legs are the base and height, so the area is simply half their product.
Why is the area half of base times height?
Any triangle is exactly half of a parallelogram or rectangle built on the same base and height, so its area is half of base times height.
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