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Irregular Trapezoid Area Calculator

Calculate the area of irregular trapezoids using bases and height

Calculate Irregular Trapezoid

What do you want to calculate?

Base A (parallel side)

Base B (parallel side)

Height (perpendicular distance)

Unit

Results

Area = 32.00 cm²

Formula Used

A = (10 + 6) × 4 / 2

Calculation

A = 16 × 4 / 2 = 32

Base A

10 cm

Base B

6 cm

Height

4 cm

Average Base

8.00 cm

(Base A + Base B) / 2

Estimated Perimeter

24.94 cm

Approximate (assumes right legs)

Step-by-Step Solution

Step 1: Identify the parallel bases: a = 10 cm, b = 6 cm

Step 2: Identify the height: h = 4 cm

Step 3: Apply the trapezoid area formula: A = (a + b) × h / 2

Step 4: Substitute values: A = (10 + 6) × 4 / 2

Step 5: Calculate: A = 16 × 4 / 2 = 32 cm²

Trapezoid Formulas

Area Formula

A = (a + b) × h / 2

Where a and b are the parallel bases, and h is the height

Height Formula

h = 2A / (a + b)

Rearranged to find height when area and bases are known

Base Formula

b = 2A/h - a

Rearranged to find one base when area, height, and other base are known

Quick Reference

Trapezoid Properties

• Has one pair of parallel sides (bases)
• Non-parallel sides are called legs
• Height is perpendicular distance between bases
• Irregular means legs have different lengths

Key Elements

• Base A: First parallel side
• Base B: Second parallel side
• Height: Perpendicular distance
• Area: Surface enclosed by trapezoid

Formula Variants

A = (a + b) × h / 2

A = h × (a + b) / 2

A = average_base × h

Example Problems

Example 1

Base A = 8 cm, Base B = 4 cm, Height = 3 cm

A = (8 + 4) × 3 / 2 = 18 cm²

Example 2

Base A = 12 m, Base B = 6 m, Height = 5 m

A = (12 + 6) × 5 / 2 = 45 m²

Example 3

Area = 24 cm², Base A = 10 cm, Base B = 6 cm

h = 2 × 24 / (10 + 6) = 3 cm

Understanding Irregular Trapezoids

What is an Irregular Trapezoid?

An irregular trapezoid is a four-sided quadrilateral with exactly one pair of parallel sides (called bases) and two non-parallel sides (called legs) of different lengths. The key feature that makes it "irregular" is that the legs are not equal in length.

Key Properties

•Has exactly one pair of parallel sides (bases)
•The legs (non-parallel sides) have different lengths
•Sum of all interior angles equals 360°
•Adjacent angles are supplementary (sum to 180°)

Area Formula Derivation

The area formula A = (a + b) × h / 2 can be understood as the area of a triangle with base equal to the sum of the trapezoid's bases and the same height.

Applications

•Architecture and construction projects
•Land surveying and property measurement
•Engineering design calculations
•Calculating material quantities

Step-by-Step Calculation Guide

Step 1: Identify

Identify the two parallel bases (a and b) and the perpendicular height (h) between them.

Step 2: Apply Formula

Use the formula A = (a + b) × h / 2, where the bases are added first, then multiplied by height and divided by 2.

Step 3: Calculate

Substitute your values and perform the calculation. Remember to include proper units in your final answer.

Common Mistakes to Avoid

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Confusing legs with bases

Only the parallel sides are bases; the slanted sides are legs and don't affect area calculation.

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Using slant height instead of perpendicular height

Height must be the perpendicular distance between the parallel bases.

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Forgetting to divide by 2

The formula includes division by 2 - don't forget this step!