Area of a Parallelogram Formula (With Examples)
Area of a Parallelogram
The area of a parallelogram is found by multiplying the length of the base by the perpendicular height. Even though a parallelogram is slanted, its area is calculated the same way as a rectangle.
📌 Area of a parallelogram formula
Let:
- b = base length
- h = perpendicular height
Area = b × h
What counts as the height?
The height must be the perpendicular distance between the two parallel sides. The slanted side length is not the height unless the shape is a rectangle.
🧮 Worked Example 1
A parallelogram has base b = 12 cm and height h = 7 cm. Find the area.
- Write the formula: Area = b × h
- Substitute values: 12 × 7
- Calculate: 84
✅ Area = 84 cm²
🧮 Worked Example 2 (height not shown directly)
A parallelogram has base 10 m and a slanted side 13 m. The perpendicular height is 8 m.
Even though the slanted side is 13 m, you must use the height:
Area = 10 × 8 = 80 m²
Relationship to other shapes
- A rectangle is a special parallelogram with right angles.
- Two congruent triangles can form a parallelogram.
- The area depends only on base and height, not the angle.
Common mistakes to avoid
- Using the slanted side instead of the perpendicular height.
- Forgetting to square the units (cm², m², etc.).
- Mixing units (convert first).
Related formulas
- Area of a triangle: ½bh
- Area of a trapezium: ½(a + b)h
- Area of a rectangle: lw
- Area of a rhombus: ½d₁d₂
Disclaimer: This page is provided for general educational reference only. While care has been taken to present accurate formulas and examples, results may vary depending on rounding and measurement precision. This content does not replace professional educational, engineering, or technical advice.