Parallelogram Area Calculator
Calculate the area of a parallelogram instantly. Enter the base and perpendicular height for step-by-step solutions.
What is the Area of a Parallelogram?
A parallelogram is a quadrilateral with two pairs of parallel sides. Its area is simply base times height (A = b × h), where the height is the perpendicular distance between the parallel sides—not the slant side length! This is the same formula as for rectangles because a parallelogram can be rearranged into a rectangle.
Area Formula
A = b × hBase times perpendicular height. Do NOT use the slant side length!
Using Two Sides + Angle
A = a × b × sin(θ)Where a and b are adjacent sides and θ is the angle between them.
Using Diagonals
A = ½ × d₁ × d₂ × sin(φ)Where d₁ and d₂ are diagonals and φ is the angle between them.
Perimeter
P = 2(a + b)Sum of all four sides (opposite sides are equal).
Examples
Basic: base 8, height 5
A = 8 × 5 = 40 square units = 40
With Angle: sides 6 and 10, angle 60°
A = 6 × 10 × sin(60°) = 60 × 0.866 ≈ 52 = ≈ 52
Rhombus: diagonals 8 and 6
A = ½ × 8 × 6 = 24 (diagonals are perpendicular in a rhombus) = 24
Tile Pattern: base 30cm, height 25cm
A = 30 × 25 = 750 cm² per tile = 750 cm²
Frequently Asked Questions
What is the formula for the area of a parallelogram?
The area of a parallelogram is A = base × height, where the height is the perpendicular distance between the two parallel bases—not the length of the slanted side.
Why is the area formula base × height, not base × side?
The slant side is longer than the height. If you 'cut' a triangle from one end and move it to the other, a parallelogram becomes a rectangle. That's why we use perpendicular height.
What is a rhombus?
A rhombus is a special parallelogram where all four sides are equal length. Its area can be calculated as A = ½ × d₁ × d₂ (half the product of diagonals) since diagonals are perpendicular in a rhombus.
Is a rectangle a parallelogram?
Yes! A rectangle is a parallelogram with all angles equal to 90°. All properties of parallelograms apply to rectangles, plus the additional right-angle property.
How do I find the height of a parallelogram?
If you know the area and base: h = A / b. Otherwise, if you know a side and an angle, use h = side × sin(angle) where the side is the slant side adjacent to the base.