Parallelogram Area Calculator - Free Geometry Calculator
Free parallelogram area calculator. Calculate area and perimeter of parallelograms using base and height. Our calculator supports squares, rectangles, and all parallelogram types with step-by-step solutions. Perfect for geometry calculations and educational use.
Last updated: October 19, 2025
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Area Result
Base
5.00 cm
Height
3.00 cm
Perimeter
16.00 cm
Type
Rectangle
Formula:
A = b × h = 5 × 3 = 15.00 cm²
The area of the parallelogram is 15.00 cm². This is a rectangle with base 5 cm and height 3 cm. The area is calculated by multiplying the base by the perpendicular height.
Step-by-Step Solution
- Given parallelogram with base = 5 cm and height = 3 cm
- Step 1: Identify the base and height
- Base (b) = 5 cm
- Height (h) = 3 cm
- Step 2: Apply the area formula
- Area = base × height
- Area = 5 × 3
- Step 3: Calculate the area
- Area = 15.00 cm²
- Step 4: Calculate perimeter (assuming rectangle/square)
- Perimeter = 2 × (base + height)
- Perimeter = 2 × (5 + 3)
- Perimeter = 2 × 8.00
- Perimeter = 16.00 cm
Parallelogram Area Calculator Types & Methods
Formula
A = base × height
Most common method using perpendicular height measurement
Formula
A = length × width
Rectangles are parallelograms where height equals adjacent side
Formula
A = s²
Squares have all sides equal and all angles 90 degrees
Methods
Base × height or ½ × diagonals
Rhombuses have equal sides but not necessarily 90° angles
Formula
P = 2(a + b)
Sum of all four sides or twice the sum of adjacent sides
Types
Squares, Rectangles, Rhombuses
All special parallelograms use the base × height formula
Quick Example Result
For a parallelogram with base = 5 cm and height = 3 cm:
Area
15 cm²
Perimeter
16 cm
How Our Parallelogram Area Calculator Works
Our parallelogram area calculator uses the fundamental geometry formula A = base × height to calculate area and perimeter. The calculation applies geometric principles to analyze quadrilaterals with opposite sides parallel. The formula works for all parallelogram types including squares, rectangles, and rhombuses.
The Parallelogram Area Formula
A = base × height = b × h (area formula)P = 2(base + adjacent side) = 2(a + b) (perimeter)Square: A = s² (all sides equal)Rectangle: A = l × w (all angles 90°)The key is using the perpendicular height, not the length of an adjacent side (unless it's a rectangle). The height is always perpendicular to the base, forming a right angle.
Shows base, perpendicular height, and how they form a rectangle
Geometric Foundation
Parallelogram area calculation is based on fundamental geometry principles. The formula derives from the fact that any parallelogram can be transformed into a rectangle with the same area by "cutting and pasting" triangular sections. This geometric transformation demonstrates why base × height works for all parallelograms.
- All parallelograms use the same area formula: A = base × height
- The height must be perpendicular to the base (forms 90° angle)
- Squares and rectangles are special types of parallelograms
- Rhombuses have equal sides but may have non-90° angles
- Parallelograms have opposite sides equal and parallel
- Diagonals of parallelograms bisect each other
Sources & References
- Geometry: Seeing, Doing, Understanding - Harold R. Jacobs (3rd Edition)Comprehensive geometry textbook covering parallelogram properties and area calculations
- Geometry for Enjoyment and Challenge - Richard Rhoad, George Milauskas, Robert WhippleDetailed coverage of quadrilateral properties and area formulas
- Khan Academy - Area of ParallelogramsEducational resources for understanding parallelogram area calculations
Need help with other geometry calculations? Check out our trapezoid calculator and rectangular prism calculator.
Get Custom Calculator for Your PlatformParallelogram Area Calculator Examples
Given Values:
- Base (b): 8 cm
- Height (h): 6 cm
- Parallelogram type: Rectangle (if angles are 90°)
Calculation Steps:
- Identify base: b = 8 cm
- Identify height: h = 6 cm
- Apply formula: A = base × height
- Calculate: A = 8 × 6 = 48 cm²
- Calculate perimeter: P = 2(8 + 6) = 28 cm
Result: Area = 48 cm², Perimeter = 28 cm
The parallelogram has an area of 48 square centimeters and a perimeter of 28 centimeters.
Square Example
Square with side = 5 cm
Area = 5 × 5 = 25 cm²
Perimeter = 4 × 5 = 20 cm
Rhombus Example
Rhombus with base = 10 cm, height = 7 cm
Area = 10 × 7 = 70 cm²
Perimeter = 4 × 10 = 40 cm
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