PanMaths.comFree Printable Math Formula Reference Sheet
Area of a Triangle
Geometry • Grades 5, 6, 7, 8, 9
Geometry
Area of a Triangle
Calculate the 2D area of any triangle using base and height, SAS trigonometry, or Heron's formula.
The Formula
A = 12bh
Used for: Finding the 2D area of any triangle using base and height, SAS trigonometry, or 3 sides (Heron's formula)
AArea of the triangle (square units)
bBase length of the triangle
hPerpendicular height to the base
sSemi-perimeter: (a + b + c) / 2
⚡Live Interactive Quick Solver
Instant CalculationTriangle Area (A):20.00 units²
Step: A = ½ × 8 × 5 = 20.00 units²
A = \frac{1}{2}bh = \frac{1}{2}ab \sin C = \sqrt{s(s-a)(s-b)(s-c)}
PDF + Answer Keys⭐ Master PDF Workbook$3.99
The Ultimate Math Formula Handbook (36-Page Master Edition)
- ✓50 curated printable worksheets in 1 PDF
- ✓100% verified step-by-step answer keys
- ✓Unlimited classroom & homeschool print license
🔒 Instant PDF Download • Secure Checkout via Gumroad & PayPal
🎯 Key Concepts & Rules
Essential principles for calculating with this formula:
📐
A = ½bh (Standard Formula)Multiply base by perpendicular height and divide by 2.
🔄
Heron's Formula (3 Sides)A = √[s(s-a)(s-b)(s-c)] where s = (a+b+c)/2.
📊
A = ½ab·sin(C) (SAS Trig)Find area when you know two sides and the included angle.
📝 Worked Examples & Step-by-Step Solutions
Example 1: Given Base & Height
Problem:
A triangle has base b = 10 cm and height h = 6 cm.1
Write Formula
A = ½ × b × h2
Substitute
A = ½ × 10 × 63
Calculate
A = ½ × 60 = 30 cm²Answer: A = 30 cm²
Example 2: Heron's Formula (Sides: 5, 6, 7)
Problem:
Find area of a triangle with sides a = 5, b = 6, c = 7.1
Semi-perimeter (s)
s = (5 + 6 + 7) / 2 = 18 / 2 = 92
Apply Heron's
A = √[9 × (9-5) × (9-6) × (9-7)]3
Multiply Terms
A = √[9 × 4 × 3 × 2] = √2164
Calculate
A ≈ 14.70 cm²Answer: A ≈ 14.70 cm²
💡 Pro Tips & Common Mistakes
Perpendicular Height Only
Height must always form a 90° right angle with the base, not the slanted side length.
Right Triangles
In a right triangle, the two legs serve directly as base and height (A = ½ab).
Equilateral Triangle Shortcut
For side length s, Area = (√3 / 4) × s².
Advertisement