GeomBench

Parallelogram Area Calculator

Base × side × sin(angle) — with a live to-scale diagram.

Base

Side

Angle between them (°)

Area

37.588

Perimeter: 26
Height: 4.699

What you entered

Base: 8Side: 5Angle: 70°

1
Height from the slant side and angle
5 × sin(70°)= 4.6985
2
Area = base × height
8 × 4.6985= 37.5877
3
Perimeter
2 × (8 + 5)= 26

Result

Area: 37.588

A parallelogram with base 8, side 5, and a 70° angle between them has an area of 37.588 and a perimeter of 26.

Parallelogram area from base, side and angle

Area is base times perpendicular height, and the height is derived from the slant side and the angle between the sides.

Base	Slant side	Angle	Height	Area	Perimeter
6	4	30 deg	2.000	12.00	20.00
6	4	45 deg	2.828	16.97	20.00
6	4	60 deg	3.464	20.78	20.00
6	4	90 deg	4.000	24.00	20.00
8	5	60 deg	4.330	34.64	26.00
10	6	45 deg	4.243	42.43	32.00
12	8	60 deg	6.928	83.14	40.00

The first four rows hold the sides fixed and change only the angle, and they show the central point: perimeter stays at 20.00 throughout while area doubles from 12.00 to 24.00. A parallelogram with the same side lengths can enclose very different areas depending on how far it leans, and it reaches maximum area at 90 degrees, where it becomes a rectangle. The height used in the formula is the perpendicular distance between the parallel sides, never the slant side itself - substituting the slant length is the usual mistake.

Why the sine shows up

A parallelogram's area is base × height, but height isn't always given directly. If you know the slant side and the angle it makes with the base, height = side × sin(angle) — so area = base × side × sin(angle) in one step.

Where this comes up

Parallelogram area appears in physics (force/torque parallelograms), land surveying for skewed plots, and engineering when components meet at an angle rather than square.

Frequently asked questions

How do I calculate the area of a parallelogram?

Area = base × height (perpendicular height, not the slant side). If you know the side and angle instead: Area = base × side × sin(angle). A parallelogram with base 10, side 6, angle 60°: Area = 10 × 6 × sin(60°) = 51.96.

What is the difference between a parallelogram and a rectangle?

A rectangle is a special parallelogram where all angles are 90°. In a general parallelogram, opposite angles are equal but not necessarily 90°. A rectangle's area = length × width; a parallelogram's area = base × height (the perpendicular distance between parallel sides).

How do I find the height of a parallelogram?

Height = Area / base. Or if you know a side and angle: height = side × sin(angle). The height is always perpendicular to the base — it's the shortest distance between the two parallel sides, not the length of the slanted side.