Triangle Area Calculator (base and height)
Calculate triangle area from base and perpendicular height.
Works for any triangle — right, obtuse, scalene, isosceles, equilateral.
Multiple units.
The base-times-height formula works for every triangle, not just right triangles.
A = ½ × b × h
Where b is any side (the base) and h is the perpendicular distance from that side to the opposite vertex. The trick is the word “perpendicular.” If you measure h along the slanted side instead of straight down to the base, you get the wrong number.
Two common ways to mess this up:
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Using a side length instead of the perpendicular height. For an isosceles triangle with two 5 cm sides and a 6 cm base, the height is not 5 — it’s about 4 cm. Drop a vertical line from the apex to the base; that vertical line is h.
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Picking a height that’s outside the triangle. For an obtuse triangle, the perpendicular from the apex sometimes falls outside the base. That’s still the right height. Extend the base line if you need to, then measure.
Where this comes up in real work:
- Roofing: the triangular gable end of a house. A 30 ft wide gable with a 12 ft peak height has area 0.5 × 30 × 12 = 180 sq ft. That’s the siding or paint area you need for one gable.
- Sail-making: triangular sails are sized this way. A 25 ft luff (vertical edge) and a 12 ft foot (bottom) give roughly 150 sq ft of sail — though sails are usually shaped curves, not perfect triangles.
- Garden beds: a corner garden bed that’s a right triangle 6 ft along the fence and 4 ft out has 12 sq ft of planting area.
If you don’t know the perpendicular height:
Use Heron’s formula instead, which works from the three sides alone. Or use the SAS formula: A = ½ × a × b × sin(C), where C is the angle between sides a and b.
Worked example — banner cut:
You’re cutting a triangular party banner. Base 36 in, height 24 in. Area = 0.5 × 36 × 24 = 432 sq in = 3 sq ft. Add 2 inches of seam allowance on each edge and the actual fabric you cut is larger.
The factor of ½ is the source of more confusion than it deserves. A triangle is exactly half of the rectangle you could draw around it (using base as width and height as height). Cut a rectangle on a diagonal — both halves have the area we compute here.