Enter any positive base length and the perpendicular height to work out the triangle’s area using the standard school formula. Useful for geometry homework and rough checks in either metric or imperial units—keep units consistent so the area is in square units of your choice.
Positive number; use the same units as height (cm, m, ft, in, etc.).
Altitude from the base to the opposite vertex, same units as base.
Enter any positive base length and the perpendicular height to work out the triangle’s area using the standard school formula. Useful for geometry homework and rough checks in either metric or imperial units—keep units consistent so the area is in square units of your choice.
Area = (1/2) × base × height Here “height” is the perpendicular distance from the base to the opposite vertex (not necessarily a slanted side length).
Base = 8 cm and perpendicular height = 5 cm. Area = ½ × 8 × 5 = 20 cm². If you use metres instead, the same numbers give 20 m²—only the unit label changes.
Multiply base by the perpendicular height, then divide by two: Area = ½ × base × height. Our tool applies that formula once both values are positive numbers.
Use the perpendicular segment from the extended base line up to the opposite vertex. If you only know side lengths, a side-and-height tool may not be enough—consider Heron’s formula instead.
The maths is unitless until you label it. Enter base and height in the same unit (both metric or both imperial); the area is then in matching square units.
No. Heron uses all three side lengths. This tool needs one base and its matching altitude—faster when you already know those two measurements.
Triangle Area Calculator: Base × Height for Homework & Quick Checks
Students in the US and UK often search for a simple triangle area rule when a diagram gives one base and a vertical (perpendicular) height. This article explains the classic Area = ½ × base × height formula in plain language and links to a calculator that applies it reliably for homework-style practice.
Pick any side as the base. The height is not a slanted edge unless that edge happens to be perpendicular to the base—it is the shortest distance from the base line to the opposite vertex. For acute and right triangles that altitude sits inside the triangle; for obtuse triangles it may fall outside, but the same numeric formula applies once you measure that perpendicular distance consistently with your chosen base. Keeping units aligned (feet with feet, centimetres with centimetres) makes the area interpretation straightforward: multiply lengths once, halve the product, and read the result in square units.
Let b be the length of the chosen base and h be the perpendicular height to that base. Then A = (1/2) × b × h.
Suppose a triangular plot has a 12 m base along a fence and the surveyor measures a 7 m perpendicular height to the corner opposite that fence. Then A = ½ × 12 × 7 = 42 m². In imperial, a 10 ft base with a 4 ft altitude gives A = ½ × 10 × 4 = 20 ft²—the calculator accepts either system as long as both inputs share it.
Open the Triangle Area (½bh) tool, type a positive base in `base_len` and the matching perpendicular height in `height_len`, then read the result lines. Errors appear if either value is missing, non-numeric, or not positive. Interpret the final number as square units that match whatever unit you used twice (cm², m², ft², in²).
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