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How to Find the Area of a Triangle

Learn triangle area formulas (½bh, Heron’s formula), avoid common mistakes, use our interactive calculator, and see real-life applications in construction, surveying, and design.

Quick Formula
The essential formula you need to know
A = ½bh
or
Area = ½ × base × height
Variables
b = base (any side of the triangle)
h = height (perpendicular distance to base)
½ = one half (0.5)
Visual Guide
b (base)h (height)Area = ½ × b × h
Interactive Calculator
Enter the base and height to calculate the area instantly

Height must be perpendicular to the base

Practice Problems
Test your understanding with these triangle area problems
Problem 1 of 4Score: 0/0

Find the area of a triangle with base 8 cm and height 6 cm.

cm²
Common Mistakes to Avoid
Learn from these frequent errors to get accurate results
Forgetting the ½ (one half)
The triangle area formula MUST include ½, not just base × height
Example: For base=6, height=4: WRONG: 6×4=24, CORRECT: ½×6×4=12
Using slant height instead of perpendicular height
Height must be perpendicular (90°) to the base, not along a slanted side
Example: In a triangle, the slant side is NOT the height - draw a perpendicular line
Unit inconsistency
Make sure base and height use the same units
Example: Don't mix cm and inches - if base is 5cm, height must also be in cm
Confusing different triangle formulas
Use ½bh for base-height, Heron's formula for three sides
Example: Don't try to use ½bh when you only know the three side lengths
How the Formula Works
Understanding the mathematical principle behind A = ½ × base × height

Rectangle Division Method

A triangle is exactly half of a rectangle with the same base and height:

Rectangle with same base and height:
hbArea = ½ × base × height

Rectangle area = base × height. Triangle area = ½ × (base × height) = ½ × base × height

Understanding Triangle Types
Different triangles, same area formula
By Sides
Equilateral: All sides equal
Isosceles: Two sides equal
Scalene: All sides different
By Angles
Right: One 90° angle
Acute: All angles < 90°
Obtuse: One angle > 90°
Key Insight

No matter what type of triangle you have, the area formula A = ½bh always works! You just need to identify the base and find the perpendicular height to that base.

Alternative Formulas
Heron's Formula: When you know all three sides
SAS Formula: ½ab sin(C) when you know two sides and included angle
Real-World Applications
See how triangle area calculations are used in everyday life

Architecture & Construction

Calculate roof areas, triangular supports, and structural elements

Example: A triangular roof section with base 20ft and height 8ft has area = ½×20×8 = 80 sq ft

Landscaping & Gardening

Plan triangular garden beds, pathways, or decorative areas

Example: A triangular flower bed with base 6ft and height 4ft needs 12 sq ft of soil

Land Surveying

Calculate areas of triangular plots of land or property boundaries

Example: A triangular lot with base 100m and height 60m has area = 3,000 square meters

Art & Design

Calculate areas for triangular designs, logos, or artistic elements

Example: A triangular logo with base 8cm and height 6cm covers 24 square centimeters
Related Problems
Continue learning with these related geometry topics
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