Area and Perimeter of a Parallelogram: Formula, Examples, and Common Mistakes

After covering rectangles, squares, triangles, and circles, the parallelogram is the natural next shape to learn — it builds directly on what you already know about rectangles and triangles. Parallelograms show up in real life in tilted rooftops, sliced bread, and certain road signs, and this topic is a regular favorite in geometry exams around the world.

What Is a Parallelogram?

A parallelogram is a four-sided shape (quadrilateral) where:

• Both pairs of opposite sides are parallel
• Opposite sides are equal in length
• Opposite angles are equal

Unlike a rectangle, a parallelogram's sides don't have to meet at right angles — it can "lean" to one side. Because of this lean, a parallelogram needs a base (b) and a perpendicular height (h) to calculate its area, along with its side length (s) to calculate perimeter.

Area of a Parallelogram

The area of a parallelogram tells you how much surface it covers.

Formula:

Area = base × height

Or simply: A = b × h

This works the same way as a triangle's area formula (minus the ÷2) because a parallelogram is essentially two identical triangles joined together.

Example 1:

A parallelogram has a base of 12 cm and a perpendicular height of 5 cm. Find its area.

• Area = b × h
• Area = 12 × 5
• Area = 60 cm²

As always, area is measured in square units (cm², m², ft²).

Perimeter of a Parallelogram

The perimeter is the total distance around all four sides.

Formula:

Perimeter = 2 × (side a + side b)

Or simply: P = 2(a + b)

This is the same idea as the rectangle's perimeter formula, since a parallelogram also has two pairs of equal, parallel sides.

Example 2:

A parallelogram has adjacent sides of 12 cm and 8 cm. Find its perimeter.

• Perimeter = 2 × (a + b)
• Perimeter = 2 × (12 + 8)
• Perimeter = 2 × 20
• Perimeter = 40 cm

Perimeter is measured in linear units (cm, m, ft).

Area vs. Perimeter: What's the Difference?

Area:

• What it measures: the space inside the parallelogram
• Formula: b × h
• Unit: square units (cm², m²)
• What you need: base and perpendicular height

Perimeter:

• What it measures: the distance around the parallelogram
• Formula: 2(a + b)
• Unit: linear units (cm, m)
• What you need: the lengths of two adjacent sides

Common Mistakes Students Make

• Using the slanted side instead of the perpendicular height for area. This is the single most common mistake — the height must always be measured straight up-and-down from the base, not along the slanted side.
• Confusing the side length with the height. In a "leaning" parallelogram, the slanted side is always longer than the perpendicular height — mixing them up gives an incorrect area.
• Forgetting that opposite sides are equal. Some students try to add all four sides individually instead of recognizing that a parallelogram only has two unique side lengths.
• Dropping the square unit for area. Writing "60 cm" instead of "60 cm²" is a frequent mistake in written exams.

Practice Problem

Try this one yourself before checking the answer:

A parallelogram-shaped field has a base of 25 meters and a perpendicular height of 14 meters. Its two adjacent sides measure 25 m and 18 m. Find both its area and perimeter.

Click to see the answer

• Area = b × h = 25 × 14 = 350 m²
• Perimeter = 2 × (25 + 18) = 2 × 43 = 86 m

Quick Recap

• Area = base × height — measured in square units, always using the perpendicular height
• Perimeter = 2 × (side a + side b) — measured in linear units

Never use the slanted side in place of the perpendicular height when calculating area

With rectangles, squares, triangles, circles, and now parallelograms covered, you've built a strong foundation across the most commonly tested 2D shapes in school geometry — the same logic extends naturally into trapezoids and other quadrilaterals next.