PanMaths.comFree Printable Math Formula Reference Sheet
Area of a Parallelogram & Rhombus
Geometry • Grades 6, 7, 8
Geometry
Area of a Parallelogram & Rhombus
Master the area formulas for parallelograms (A = bh) and rhombuses (A = ½ d₁ d₂).
The Formula
A = b × h
Used for: Finding the area of a parallelogram (A = bh) or rhombus (A = ½ d₁ d₂)
AArea of the quadrilateral
bBase length
hPerpendicular height
d₁, d₂Diagonals of a rhombus
⚡Live Interactive Quick Solver
Instant CalculationParallelogram Area (A):40.00 units²
Step: A = 8 × 5 = 40.00 units²
A = b \cdot h = \frac{1}{2} d_1 d_2
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🎯 Key Concepts & Rules
Essential principles for calculating with this formula:
▰
Parallelogram: A = bhBase multiplied by perpendicular height.
💎
Rhombus: A = ½ d₁ d₂Half the product of the two diagonals.
📐
Slant Height ≠ Vertical HeightNever multiply base by the slanted side.
📝 Worked Examples & Step-by-Step Solutions
Example 1: Parallelogram Area
Problem:
Base b = 12 cm, perpendicular height h = 7 cm.1
Apply Formula
A = b × h2
Substitute
A = 12 × 73
Calculate
A = 84 cm²Answer: A = 84 cm²
Example 2: Rhombus Diagonal Area
Problem:
Diagonals d₁ = 10 cm and d₂ = 16 cm.1
Apply Formula
A = ½ × d₁ × d₂2
Multiply
A = ½ × 10 × 163
Calculate
A = ½ × 160 = 80 cm²Answer: A = 80 cm²
💡 Pro Tips & Common Mistakes
Rectangle is a Parallelogram
When the angle is 90°, height equals side length (A = l × w).
Rhombus Diagonals
The diagonals of a rhombus always bisect each other at a 90° perpendicular angle.
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