Parallelogram Calculator

A parallelogram has two pairs of parallel sides. Its area depends on the perpendicular height, not the slanted side.

Parallelogram

Area40
Perimeter
30
Angles
53.1301° and 126.8699°

Working

  1. A = b × h = 10 × 4 = 40
  2. P = 2(b + s) = 30
  3. sin θ = h ÷ s = 0.8

Formulas

area = base × height

perimeter = 2(base + side)

acute angle = arcsin(height ÷ side)

Worked example

Base 10, side 5, height 4

  1. Area: 10 × 4 = 40
  2. Perimeter: 2 × (10 + 5) = 30
  3. Angle: arcsin(4 ÷ 5) ≈ 53.13°, so the angles are 53.13° and 126.87°

Area 40, perimeter 30.

Why base × height works

Cut the triangle off one end and slide it to the other: the parallelogram becomes a rectangle with the same base and height. That is also why the height can never be longer than the slanted side.