Parallelogram Area Calculator
Calculate the area of a parallelogram instantly. Enter the base and perpendicular height for step-by-step solutions.
Area Formula
A = b ร hBase times perpendicular height. Do NOT use the slant side length!
Using Two Sides + Angle
A = a ร b ร sin(ฮธ)Where a and b are adjacent sides and ฮธ is the angle between them.
Using Diagonals
A = ยฝ ร dโ ร dโ ร sin(ฯ)Where dโ and dโ are diagonals and ฯ 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 ร 5 = 40 square units = 40
With Angle: sides 6 and 10, angle 60ยฐ
A = 6 ร 10 ร sin(60ยฐ) = 60 ร 0.866 โ 52 = โ 52
Rhombus: diagonals 8 and 6
A = ยฝ ร 8 ร 6 = 24 (diagonals are perpendicular in a rhombus) = 24
Tile Pattern: base 30cm, height 25cm
A = 30 ร 25 = 750 cmยฒ per tile = 750 cmยฒ
Frequently Asked Questions
What is the formula for the area of a parallelogram?
The area of a parallelogram is A = base ร height, where the height is the perpendicular distance between the two parallel basesโnot the length of the slanted side.
Why is the area formula base ร height, not base ร 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 = ยฝ ร dโ ร dโ (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 90ยฐ. 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 ร sin(angle) where the side is the slant side adjacent to the base.