Parallelogram Area Calculator
Calculate the area and perimeter of a parallelogram: A = base × height
Enter Base, Height, and Side
Perimeter: 28.00 units
Calculations:
Area: A = base × height = 8 × 5 = 40.00 square units
Perimeter: P = 2(base + side) = 2(8 + 6) = 2 × 14 = 28.00 units
Parallelogram Formulas
Area: A = b × h
Perimeter: P = 2(b + s)
where: - b = length of the base - h = perpendicular height (not the slant side) - s = length of the slant side
How to Calculate Parallelogram Area
- Identify the base: Choose one side of the parallelogram
- Find the height: Measure the perpendicular distance from the base to the opposite side (not the slant length)
- Multiply: Area = base × height
- For perimeter: Add base and side, then multiply by 2
Why the Formula Works
A parallelogram can be rearranged into a rectangle by cutting a triangle from one end and moving it to the other. The resulting rectangle has the same base and height, so the area is simply base × height.
Real-World Applications
Parallelogram calculations are used in: - Architecture: Window and door frame designs - Engineering: Force vector diagrams - Physics: Understanding shear forces - Tiling and flooring: Diagonal tile patterns - Graphic design: Creating perspective effects
Common Questions
What is the formula for parallelogram area?
The parallelogram area formula is A = base × height, where base is the length of one side and height is the perpendicular distance to the opposite side.
How is a parallelogram different from a rectangle?
A rectangle is a special parallelogram where all angles are 90 degrees. In a general parallelogram, opposite angles are equal but not necessarily 90 degrees. Both use the same area formula: base × height.