What is the formula for Area of a Trapezoid?

The mathematical formula for Area of a Trapezoid is A = ½(a + b)h. It is used for calculating the area enclosed by a trapezoid (trapezium) given its two parallel bases and height.

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Area of a Trapezoid

Geometry • Grades 6, 7, 8, 9

Geometry

Area of a Trapezoid

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

In the formula A = ½(a + b)h: A = Area of the trapezoid (square units), a = Length of top parallel base, b = Length of bottom parallel base, h = Perpendicular height between the bases.

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

To calculate area of a trapezoid: 1. Identify the given values (A = Area of the trapezoid (square units), a = Length of top parallel base, b = Length of bottom parallel base, h = Perpendicular height between the bases). 2. Substitute the values into the formula A = ½(a + b)h. 3. Simplify and evaluate step-by-step.

Learn how to calculate the area of any trapezoid (trapezium) given its parallel bases and height.

The Formula

A = 12(a + b)h

Used for: Calculating the area enclosed by a trapezoid (trapezium) given its two parallel bases and height

AArea of the trapezoid (square units)

aLength of top parallel base

bLength of bottom parallel base

hPerpendicular height between the bases

⚡Live Interactive Quick Solver

Instant Calculation

Base a:

Base b:

Height (h):

Trapezoid Area (A):32.00 units²

Step: A = ((6 + 10) / 2) × 4 = 8 × 4 = 32.00

A = \frac{a + b}{2} \cdot h

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🎯 Key Concepts & Rules

Essential principles for calculating with this formula:

⏢Average of the Bases

Add the two parallel bases (a + b) and divide by 2.

📏Perpendicular Height (h)

The straight vertical distance between the two parallel bases.

✓Units Squared

Always express the final area in square units (cm², m², in²).

📝 Worked Examples & Step-by-Step Solutions

Example 1: Standard Trapezoid Area

Problem: Top base a = 6 cm, bottom base b = 10 cm, height h = 4 cm.

Write FormulaA = ½ × (a + b) × h

Add Basesa + b = 6 + 10 = 16 cm

SubstituteA = ½ × 16 × 4

CalculateA = 8 × 4 = 32 cm²

Answer: A = 32 cm²

Example 2: Finding Missing Height

Problem: Area = 50 cm², parallel bases are 8 cm and 12 cm. Find height h.

Set Up Equation50 = ½ × (8 + 12) × h

Simplify50 = ½ × (20) × h = 10h

Solve for hh = 50 / 10 = 5 cm

Answer: h = 5 cm

💡 Pro Tips & Common Mistakes

Why the formula works

A trapezoid is half of a parallelogram with base (a + b) and height h.

Isosceles Trapezoid

The non-parallel slanted legs are equal in length, creating symmetric angles.

Order of Bases Doesn't Matter

Whether you label top or bottom as "a" or "b", the sum (a + b) remains identical.

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