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How to Find the Area of a Trapezoid

Learn the formula, common mistakes, interactive calculator, and real-life applications.

Get quick answers and deep understanding of trapezoid area calculations.

Quick Formula
The essential formula you need to know
A = ½(b₁ + b₂)h
or
Area = ½ × (base₁ + base₂) × height
Variables
b₁, b₂ = lengths of the two parallel sides (bases)
h = height (perpendicular distance between bases)
½ = one half (0.5)
Visual Guide
b₁b₂h
Interactive Calculator
Enter the parallel sides and height to calculate the area instantly

Perpendicular distance between parallel sides

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

Find the area of a trapezoid with parallel sides of 8 cm and 12 cm, and height 5 cm.

cm²
Common Mistakes to Avoid
Learn from these frequent errors to get accurate results
Using slant height instead of perpendicular height
Height must be the perpendicular distance between the parallel sides, not the slanted side length
Example: If the slant side is 5 and the perpendicular height is 4, use h = 4, not h = 5
Forgetting the ½ factor
The formula is ½(b₁ + b₂)h, not just (b₁ + b₂)h
Example: For bases 6 and 10, height 4: Area = ½(6+10)×4 = 32, not 64
Confusing which sides are parallel
Only use the parallel sides (bases) in the formula, not the slanted sides
Example: In a trapezoid with sides 5, 8, 6, 10 - identify which two are parallel first
How the Formula Works
Understanding the mathematical principle behind A = ½(b₁ + b₂)h

Average Base Method

A trapezoid can be thought of as a rectangle with the average of the two parallel sides as its width:

Trapezoid visualization:

Trapezoid Area Formula: A = ½(b₁ + b₂)h

Trapezoid

b₁ = 80b₂ = 120h = 60

Average Base Method

Average Base = (80 + 120) ÷ 2 = 100Average Base = 100h = 60

How the Formula Works

Average Base Method: A trapezoid can be thought of as a rectangle with the average of the two parallel sides as its width.

Average base = (b₁ + b₂) ÷ 2 = (80 + 120) ÷ 2 = 100
Area = average base × height = 100 × 60 = 6000
Or using the original formula: A = ½(b₁ + b₂)h = ½(80 + 120) × 60 = 6000

This formula works because a trapezoid is essentially a rectangle with width equal to the average of the two parallel sides.

Average base = (b₁ + b₂) ÷ 2
Area = average base × height = ½(b₁ + b₂) × h

This formula works because a trapezoid is essentially a rectangle with width equal to the average of the two parallel sides.

Real-World Applications
See how trapezoid area calculations are used in everyday life

Architecture & Roofing

Calculate areas of trapezoidal roof sections and building facades

Example: A roof section with bases 12m and 8m, height 5m has area = ½(12+8)×5 = 50 m²

Civil Engineering

Find cross-sectional areas of channels, dams, and embankments

Example: A trapezoidal channel with top width 6ft, bottom width 4ft, depth 3ft has area = 15 ft²

Automotive Design

Calculate areas of trapezoidal car windows and body panels

Example: A car windshield with top 48 inches, bottom 52 inches, height 30 inches covers 1,500 in²

Manufacturing

Determine material areas for trapezoidal metal sheets and components

Example: A metal bracket with parallel edges 8cm and 12cm, height 6cm needs 60 cm² of material
Related Problems
Continue learning with these related geometry topics
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