Area of a Trapezoid Calculator

Welcome to our Online Trapezoid Area Calculator! This is a simple and easy-to-use free tool that requires no registration or download. Just enter the top base, bottom base, and height of the trapezoid to instantly calculate the precise area. Whether you're a student completing math homework or an engineer or designer working on professional projects, this tool can save you valuable time.

Trapezoid Area Calculation Formula

This tool uses the internationally standard trapezoid area formula for calculation:

Area = (Top Base + Bottom Base) × Height ÷ 2

Letter representation: A = (b + a) × h ÷ 2

A represents the area of the trapezoid.

a represents the length of the bottom base in this tool.

b represents the length of the top base in this tool.

h represents the height of the trapezoid (the perpendicular distance between the two parallel bases).

Formula principle: The essence of this formula is to find the average of the two base lengths ((a+b)/2) and then multiply by the height. It can be understood as combining two identical trapezoids to form a parallelogram with (a+b) as the base and h as the height, where the area of the original trapezoid is exactly half of this parallelogram.

Frequently Asked Questions

Q1: What is a trapezoid?

A1: A trapezoid is a quadrilateral with at least one pair of parallel sides. Typically, when we refer to a trapezoid, we mean one with only one pair of parallel sides. The parallel sides are called the "bases" (top base and bottom base), and the non-parallel sides are called the "legs".

Q2: Why is the calculation formula (Top Base + Bottom Base) × Height ÷ 2?

A2: As mentioned above, this formula derives from geometric deduction. The most intuitive way to understand it is to duplicate the trapezoid, rotate it 180 degrees, and combine it with the original to form a parallelogram. The base of this parallelogram is (top base + bottom base), and the height remains unchanged, so the total area is (a+b)*h. The area of the original trapezoid is exactly half of this, hence the division by 2.

Q3: If the height unit is centimeters, what is the unit of the calculated area?

A3: In our calculator, regardless of the input length units, the final calculation results are displayed in square meters (m²). You can then select to convert to other area units as needed.

Q4: Is this calculator suitable for isosceles or right trapezoids?

A4: Yes, absolutely. All types of trapezoids (regular, isosceles, right-angled) use the same area formula. As long as you can accurately measure the lengths of the two parallel sides and the perpendicular height between them, this formula is correct.

Q5: If I only know the lengths of the two legs and the height of the trapezoid, can I calculate the area?

A5: Not directly. The formula requires knowing the lengths of both bases. If you don't know the exact base lengths but only know the leg lengths and height, you need to use other geometric knowledge like the Pythagorean theorem to first find the base lengths before using this tool for calculation.

Q6: Is this calculator free? Does it require installation?

A6: Yes, this is a completely free online tool that requires no download or software installation. You can use it directly by opening the webpage in your browser, whether on a computer, phone, or tablet - it's very convenient.