Area of a Parallelogram
Reference for parallelogram area formulas A = base × height and A = ab sin(θ).
Covers perimeter (2a+2b), rectangles, rhombuses, and worked examples.
The Formula
A = b × h
The area of a parallelogram equals its base multiplied by its perpendicular height.
Note: the height is NOT the slanted side — it is the perpendicular distance between the base and its opposite side.
Variables
| Symbol | Meaning |
|---|---|
| A | Area of the parallelogram |
| b | Length of the base |
| h | Perpendicular height (measured at 90° to the base) |
Example 1
Find the area of a parallelogram with base 9 cm and height 5 cm
A = b × h = 9 × 5
A = 45 cm²
Example 2
A parallelogram-shaped tile has a base of 15 inches and a height of 8 inches. What is its area?
A = b × h = 15 × 8
A = 120 square inches
When to Use It
Use the area of a parallelogram formula when:
- Calculating the area of slanted rectangular shapes
- Working with tiling or flooring patterns that use parallelogram shapes
- Solving geometry problems involving parallelograms
- Remember: a rectangle is a special case of a parallelogram (with h equal to the side length)
Key Notes
- The height h is the perpendicular distance between parallel sides — not the slanted side length; using the slant side overestimates area; h = slant × sin(θ) if only the slant is known
- When the angle θ between adjacent sides is known: A = a × b × sin(θ); a rectangle is the special case where θ = 90° and sin(90°) = 1, giving A = b × h
- A parallelogram and a rectangle with the same base and height have identical areas — mentally "sliding" the top edge horizontally doesn't change the area, only the shape
- Perimeter uses the actual side lengths, not the height: P = 2(a + b); confusing h with side length b when computing perimeter is a common error