Triangle Area Calculator
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Triangle area formula explained
The area of a triangle is A = ½ × base × height. The base can be any side, but the height must be measured at a right angle to that base. This perpendicular height is the most important detail in the calculation.
This calculator is useful for roof sections, triangular garden beds, signs, fabric cuts, diagrams, and school geometry problems where the base and height are known.
Worked example: base 10 cm, height 6 cm
A = ½ × b × h
A = ½ × 10 × 6
Result: 30 cm²
Which height should I use?
Use the vertical or perpendicular height, not a slanted side. In an obtuse triangle, the perpendicular height may land outside the triangle. The formula still works as long as the height is measured at 90 degrees to the base line.
Common mistakes
- Using a slanted side as the height.
- Forgetting the one-half factor.
- Changing the base but not changing the matching perpendicular height.
Related calculators
Step-by-step method
- Choose a side to use as the base.
- Measure the perpendicular height from that base to the opposite point.
- Multiply base by height.
- Divide the result by two.
Second example: base 7 ft, height 3.5 ft
A = ½ × b × h
A = ½ × 7 × 3.5
Result: 12.25 ft²
Practical interpretation
Triangle area is helpful when estimating parts of irregular shapes. Many real-world layouts can be split into rectangles and triangles. Calculate the rectangle portions, calculate the triangular portions, and add the results.
For a right triangle, the two sides that meet at the right angle can be used directly as base and height. For other triangles, be careful to find the perpendicular height rather than relying on a sloped edge.
How to calculate this measurement
Triangle area is half of a rectangle or parallelogram with the same base and height. The height must be perpendicular to the chosen base, even if that perpendicular line falls outside the triangle.