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Essential Geometry Formulas and How to Use Them
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Geometry formulas are useful for construction, design, architecture, gardening, and countless everyday tasks. This guide covers the most common shapes with formulas and examples.
2D Shapes: Area and Perimeter
Rectangle:
• Area = length × width
• Perimeter = 2(length + width)
Example: 6m × 4m room → Area = 24 m², Perimeter = 20 m
Circle:
• Area = π × r² (π ≈ 3.14159)
• Circumference = 2π × r
Example: radius 5 cm → Area ≈ 78.54 cm², Circumference ≈ 31.42 cm
Triangle:
• Area = ½ × base × height
• Perimeter = sum of all three sides
Example: base 10 cm, height 6 cm → Area = 30 cm²
Trapezoid:
• Area = ½ × (a + b) × height (a and b are parallel sides)
3D Shapes: Volume and Surface Area
Rectangular Box (Cuboid):
• Volume = l × w × h
• Surface Area = 2(lw + lh + wh)
Example: 3m × 2m × 1.5m → Volume = 9 m³
Sphere:
• Volume = (4/3) × π × r³
• Surface Area = 4π × r²
Example: r = 3 cm → Volume ≈ 113.1 cm³, SA ≈ 113.1 cm²
Cylinder:
• Volume = π × r² × h
• Surface Area = 2πr(r + h)
Example: r = 5 cm, h = 10 cm → Volume ≈ 785.4 cm³
Cone:
• Volume = (1/3) × π × r² × h
• Slant height l = √(r² + h²)
The Pythagorean Theorem
For any right triangle: a² + b² = c²
Where c is the hypotenuse (side opposite the right angle).
Example: legs of 3 and 4.
c² = 9 + 16 = 25
c = 5
This (3-4-5) is the most famous Pythagorean triple. Others include 5-12-13 and 8-15-17.
Try the Geometry Calculator.
Frequently Asked Questions
When should I use the perimeter vs. the area?
Perimeter measures the total boundary length—useful for fencing, framing, or edging. Area measures the 2D space inside—useful for flooring, painting, or covering.
How do I find the area of an irregular shape?
Divide the irregular shape into simpler shapes (rectangles, triangles), calculate each area separately, and sum them. Alternatively, use coordinate geometry (the Shoelace formula) if you have the vertex coordinates.