Triangle – Area
A triangle’s area is half its base times its perpendicular height: A = ½ × b × h.
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A triangle is a three-sided figure whose three angles always add up to 180°. Its area is found with A = ½ × b × h, where b is the base and h is the height. The ½ is built in because a triangle is exactly half of a parallelogram with the same base and height.
The height (h) is the perpendicular distance from the base straight up to the opposite vertex — it must form a right angle with the base. The height is never the length of a slanted side; it is the straight-up measurement.
Don’t confuse area with perimeter: area uses ½ × b × h and is measured in square units, while perimeter is the sum of all three sides in linear units. The triangle’s type (scalene, isosceles, equilateral) does not change either formula.
Worked example
A triangle has base 10 and height 6. Find its area.
- Write the formula: A = ½ × b × h.
- Substitute the values: A = ½ × 10 × 6.
- Calculate: ½ × 10 = 5, and 5 × 6 = 30.
30 square units
On the test: Area is measured in square units; use the perpendicular height, never a slanted side length.
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