Triangle Area Calculator
Quickly find the area of any triangle when you know its base and perpendicular height. Perfect for geometry problems, land surveying, construction layout, and architectural design.
About this calculator
The area of a triangle is exactly half the area of a rectangle with the same base and height. This gives us the formula A = ½ × base × height, where the height must be the perpendicular (vertical) distance from the base to the opposite vertex, not the length of a slanted side. This formula works for all triangle types — scalene, isosceles, equilateral, right-angled, and obtuse — as long as you use the true perpendicular height. If you only know the three side lengths, Heron's formula is an alternative approach. The factor of ½ comes from the geometric proof that any triangle can be doubled to form a parallelogram, so its area is half of base × height.
How to use
Suppose a triangular plot of land has a base of 14 meters and a perpendicular height of 9 meters. Enter 14 in the Base field and 9 in the Height field. The calculator computes A = 0.5 × 14 × 9 = 0.5 × 126 = 63 square meters. The plot covers 63 m². If you were seeding the land at a rate of 50 g of seed per m², you would need 63 × 50 = 3,150 g (3.15 kg) of seed. Changing either value instantly updates the area.
Frequently asked questions
How do I find the height of a triangle if it is not given?
If the perpendicular height is not directly stated, you can calculate it using trigonometry if you know an angle and a side. For a right triangle, the height is simply one of the two shorter sides (legs). For other triangles, you can drop a perpendicular from a vertex to the opposite base and use the sine rule: height = side × sin(angle). Alternatively, if all three sides are known, Heron's formula gives you the area without needing the height explicitly.
Why does the triangle area formula use one half times base times height?
A triangle can always be paired with an identical copy of itself to form a parallelogram (or rectangle for right triangles). The parallelogram has area = base × height, so each triangle is exactly half of that, giving A = ½ × base × height. This geometric proof holds for all triangle types. The key insight is that the height must be perpendicular to the chosen base, not a slanted side length.
What is the difference between the base and the height in a triangle area calculation?
The base is any side of the triangle that you choose as the reference line — usually the bottom side. The height is the perpendicular distance from that base to the opposite vertex, measured at a 90° angle. For an acute triangle, the height falls inside the triangle. For an obtuse triangle, the height may fall outside the triangle when extended. Mixing up slanted side lengths with the true perpendicular height is a common mistake that leads to incorrect area calculations.