Parallelogram Area Formula

A = base × height, plus perimeter and special cases

Reviewed by [email protected], Geometry Calculator Developer & Online Math Educator Last updated May 8, 2026

Parallelogram area = base × perpendicular height (A = b·h). The base is any one side; the height is the straight perpendicular distance to the opposite side — not the slanted side length. A parallelogram with base 8 cm and height 5 cm has area 40 cm². This is the same formula as a rectangle, because a rectangle is a parallelogram with 90° angles. Below are the 4 ways to compute area depending on what you know, plus a free calculator and worked examples.

The Formulas

Name	Formula	Notes
Area (base × height)	`A = b × h`	b = base, h = perpendicular distance between the two parallel sides.
Area (sides × angle)	`A = a × b × sin(θ)`	a, b = the two adjacent sides; θ = angle between them.
Area (diagonals)	`A = ½ × d₁ × d₂ × sin(α)`	d₁, d₂ = diagonals; α = angle between them.
Perimeter	`P = 2(a + b)`	a, b = the two different side lengths.
Height from Side + Angle	`h = a × sin(θ)`	When you have a side and its angle to the base.
Parallelogram Law	`2a² + 2b² = d₁² + d₂²`	Sum of squared sides = sum of squared diagonals (÷ 2).

Worked Examples

Example 1: Parallelogram with base 8 cm and height 5 cm

Identify the base (b = 8 cm) and the perpendicular height (h = 5 cm).
Multiply: A = b × h = 8 × 5.
Area = 40 cm². (Height is the perpendicular distance, not the slanted side.)

Example 2: Parallelogram with sides 6 and 10, angle 60°

Use the side × angle formula: A = a × b × sin(θ).
A = 6 × 10 × sin(60°).
sin(60°) = √3 / 2 ≈ 0.866.
A = 60 × 0.866 ≈ 51.96 cm². Perimeter = 2(6 + 10) = 32 cm.

Example 3: Parallelogram with diagonals 12 and 8, angle 45° between them

Use the diagonals formula: A = ½ × d₁ × d₂ × sin(α).
A = ½ × 12 × 8 × sin(45°).
sin(45°) = √2 / 2 ≈ 0.707.
A = ½ × 96 × 0.707 ≈ 33.94 cm².

Frequently Asked Questions

What is the parallelogram area formula?

The parallelogram area formula is A = b × h, where b is the length of any base and h is the perpendicular height to that base. If you know two adjacent sides a, b and the angle θ between them, use A = a × b × sin(θ).

Why is height not the same as the slanted side?

The "height" in A = b × h must be measured PERPENDICULAR to the base, not along the slanted side. Using the slant length instead gives a number larger than the true area. To get the perpendicular height from a slanted side: h = side × sin(angle to base).

How do I find the perimeter of a parallelogram?

Perimeter = 2(a + b), where a and b are the two distinct side lengths. Opposite sides of a parallelogram are always equal, so you only need two side measurements.

Is a rectangle a parallelogram?

Yes — a rectangle is a parallelogram whose interior angles are all 90°. The area formula A = b × h simplifies to A = length × width for a rectangle because the perpendicular height equals the side length when the angle is 90°.

What if I only know the two diagonals?

Use A = ½ × d₁ × d₂ × sin(α), where d₁ and d₂ are the two diagonal lengths and α is the angle between them. For a rhombus the diagonals are perpendicular (α = 90°, sin α = 1), so it simplifies to A = ½ × d₁ × d₂.