Area of a Trapezoid Calculator

Trapezoids are geometric shapes having two parallel sides of different lengths. These shapes are commonly found in various everyday objects and structures. For example, some rooftops of buildings and highway signs are designed with trapezoidal shapes. Trapezoids also appear in certain road signs, such as warning or directional signs, to capture attention and provide clear information to drivers, pedestrians, and cyclists.

Are you a student struggling to remember geometry formulas? 

Our area of a trapezoid calculator can be a helpful tool that will simplify the process of calculating the area of a trapezoid for you. It will allow you to determine other properties, such as side lengths and internal angles. This free online area of a trapezoid calculator computes the trapezoid's area quicker and more efficiently.

What is a Trapezoid?

A trapezoid is a type of quadrilateral with two parallel sides and two non-parallel sides. This two-dimensional figure is also referred to as a trapezium. The parallel sides are called the bases of the trapezoid, while the non-parallel sides are referred to as the legs or lateral sides. The distance between the parallel sides is known as the altitude. The sum of all internal angles of a trapezoid equals 360°. Additionally, the angles on the same side of a leg are called adjacent angles and always add up to 180°.

How to Calculate the Area of a Trapezoid?

To calculate the area of a trapezoid, you first find the average of the two bases and then multiply it by the altitude. The area of trapezoid formula is:

Area of Trapezoid Formula = ½ x (a + b) x h

This trapezoid area formula is based on the concept that a trapezoid's area is similar to a rectangle's area. The expression (base 1 + base 2) / 2 represents the width of a rectangle with the same area as the trapezoid. To use the area of a trapezoid calculator, you need three measurements, all in the same units (make sure to convert them if necessary).

Let us try to understand the concept better with the help of an area of a trapezoid example:

Example: Suppose one base of a trapezoid is 8 cm, the other base is 12 cm, and the height is 5 cm. To calculate the area, use the formula:

Area of Trapezoid Formula = ½ x (a + b) × h 

Substituting the values:

Area = (8 + 12) × 5 / 2 = 20 × 5 / 2 = 100 / 2 = 50 cm²

Thus, the area of the trapezoid is 50 cm2.

How to Find the Area of a Trapezoid?

To find the area of the trapezoid, you can follow the steps given below:

• Step 1: Measure the length of both bases (a and b).

• Step 2: Measure the height of the trapezoid (h).

• Step 3: Substitute these values into the formula: A = ½ x (a + b) × h.

If the trapezoid has equal bases (a = b) and the sides are equal (c = d = h), the formula simplifies to A = a × h, the same as the area formula for a rectangle.

How to Use Area of a Trapezoid Calculator?

Let us look at the steps on how to use the calculator:

• Step 1: Measure the lengths of the two bases of the trapezoid.

• Step 2: Calculate the height by constructing a right angle from one of the bases. Use the base as one of the arms to measure the perpendicular distance between the parallel sides.

• Step 3: Convert all measurements to the same units (e.g., centimetres or inches) if necessary.

• Step 4: Enter the values for the two bases and the height into the online calculator.

• Step 5: The calculator will use the formula and provide you with the area of the trapezoid.

Summing Up

Trapezoids are common geometric shapes that can be used in various fields of design and architecture. Due to their distinctive features, they can easily be considered different from other quadrilaterals. It may seem quite complicated to arrive at the area of any given trapezoid sometimes, but with the help of our area of a trapezoid calculator, it can be accomplished in no time. This online tool solves the formula for you and helps you easily find other properties of a shape, including area, side, or angles.

FAQs

What is the area of the trapezium?

The area of trapezoid is given by the formula 

Area of Trapezium = ½ x (a + b) × h.

How do you find the area of a trapezoid?

You can find the area of the trapezoid by using the area of trapezoid formula, which is

Area of Trapezium = ½ x (a + b) × h. 

What is the formula for the area of a trapezoid?

The equation gives the formula for the area of a trapezoid:

Trapezoid Area Formula = ½ x (a + b) × h

Where a+b is the sum of the bases, and h stands for the shape's height.

How is a trapezoid different from other quadrilaterals?

A trapezoid differs from other quadrilaterals since two sides (bases) are parallel, while the other sides are not. However, compared to other quadrilaterals like a parallelogram, the two pairs of opposite sides are parallel, which is not true with a trapezoid.