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Area of a Triangle

Geometry • Grades 5, 6, 7, 8, 9

Geometry

Area of a Triangle

Q: What is the formula for Area of a Triangle?

The mathematical formula for Area of a Triangle is A = ½bh. It is used for finding the 2d area of any triangle using base and height, sas trigonometry, or 3 sides (heron's formula).

Q: What do the variables in the Area of a Triangle formula represent?

In the formula A = ½bh: A = Area of the triangle (square units), b = Base length of the triangle, h = Perpendicular height to the base, s = Semi-perimeter: (a + b + c) / 2.

Q: How do you calculate Area of a Triangle step-by-step?

To calculate area of a triangle: 1. Identify the given values (A = Area of the triangle (square units), b = Base length of the triangle, h = Perpendicular height to the base, s = Semi-perimeter: (a + b + c) / 2). 2. Substitute the values into the formula A = ½bh. 3. Simplify and evaluate step-by-step.

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 Calculation

Base (b):

Height (h):

Triangle 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)}

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🎯 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.

Write FormulaA = ½ × b × h

SubstituteA = ½ × 10 × 6

CalculateA = ½ × 60 = 30 cm²

Answer: 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.

Semi-perimeter (s)s = (5 + 6 + 7) / 2 = 18 / 2 = 9

Apply Heron'sA = √[9 × (9-5) × (9-6) × (9-7)]

Multiply TermsA = √[9 × 4 × 3 × 2] = √216

CalculateA ≈ 14.70 cm²

Answer: 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.

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