In these formulas, height means the shortest perpendicular distance from a base to the opposite vertex or parallel side. It is a relationship between lines, not simply whichever side looks vertical on a drawing.

The three area formulas use the same perpendicular distance

For a triangle, A = b × h ÷ 2. For a parallelogram, A = b × h. For a trapezoid, A = (b₁ + b₂) × h ÷ 2, where b₁ and b₂ are the parallel sides. In every formula, h is measured at 90° to the selected base, and base and height must use the same length unit.

A triangle can use different bases, each with its own height

Any side may be chosen as the base, but the entered height must meet that same base at 90°. Using another side length as height is valid only for a right triangle whose sides are perpendicular.

The perpendicular may meet an extension of the base

In an obtuse triangle, the 90° foot can fall outside the side segment. Extend the chosen base as a straight line and measure the perpendicular distance from that line to the opposite vertex. The formula still uses the length of the original side as b, not the extended line.

For parallelograms and trapezoids, height spans the parallel lines

A parallelogram's slanted side is generally longer than its perpendicular height. In a trapezoid, the two values called bases must be parallel, and height is the perpendicular gap between them.

Worked examples separate the formula from the drawing

A triangle with b = 12 cm and h = 5 cm has A = 12 × 5 ÷ 2 = 30 cm². A parallelogram with the same base and height has A = 12 × 5 = 60 cm². A trapezoid with parallel bases 8 cm and 14 cm and h = 5 cm has A = (8 + 14) × 5 ÷ 2 = 55 cm².

Two quick checks catch a mismatched height

First, identify the right-angle mark between h and the exact base used as b. Second, calculate again with another valid base-height pair when the figure provides one: the base and height values may change, but the area must not. If every length is scaled by k, the area should scale by k².

The calculator cannot verify the angle of your measurement

AreaCalc applies the formula to numbers you supply. It does not inspect a plan, image, coordinate set, or physical object, so verify perpendicularity with the appropriate drawing or measuring method before relying on the result.