You know about the importance of shapes in mathematics.  There are many shapes i.e trapezoid, circle or square etc you know about. Maybe you have seen them in books like math, physics. All of these shapes are important. Shapes have been given greater importance, especially in math and physics.

Here, we will discuss the fact of what we need to know about trapezoid and arc length? If we talk about trapezoids, somehow you are already familiar with them. It consists of shapes that consist of four parallel sides.

Arc length is also important because it is also related to shape. Have you seen a circle? Or any curved shape? Arc length is used to find out the curve of a circle. Now we will focus on the trapezoid area and arc length to clear our concepts further. 

What is a trapezoid?

The shape which has quadrilateral sides with two sides parallel to each other is known as a trapezoid. It means it consists of four sides and has a closed shape. Trapezoid shape has four interior angles and four-segment lines. Also, it contains two bases and two legs. The parallel sides are its two bases and the other two sides are its legs.

Usually, trapezoids have longer parallel sides, these are base and it is horizontal. If you draw a line perpendicular from the base to the other parallel side, then it will give you the trapezoid’s height or altitude.

How to Find the Area of a Trapezoid?

If you want to find out the area of the trapezoid first you need to know about the base and altitude of the trapezoid. After this label the four sides. 

For example:

If you have a trapezoid and you want to find out its area, label all four sides with words or numbers, for example, if you have one parallel side longer than others give it to label a, and give label b to the shorter side.

Now label the perpendicular sides. Label a line perpendicular to the two bases with the letter h, h is for height or altitude of the trapezoid.

But we can also calculate it by using a trapezoid angle calculator.

What is arc length?

The measure of the distance along the curved line that makes up the arc is known as arc length. It looks like a chord because it has a longer distance than a straight line between its endpoints.

The central angle in degrees:

The formula for the arc measure is:

Arc length=2πR (C/360)

Where:

• C  is the central angle of the arc in degrees
• R  is the radius of the arc
• π  is Pi, approximately 3.142

You may already know that 2πR is the circumference of the whole circle. Therefore you can simply reduce the by formula ratio of the arc to the full angle, which is 360. With the help of the above-mentioned formula, you can find out the central angle, radius, or arc length. Arc length calculator with steps helps us to find the length of any arc online.

The central angle in radians*:

Now we will see how we can find out the central angle in the radius. For this we will use a simple formula that is given below:

Arc length=RC 

Where:

• C is the central angle of the arc in radians.
• R  is the radius of the arc

We are using the almost same formula for this as we have used for degrees but here we are making some difference like the 2π/360 converts the degrees to radians.

We can also use radians to find out the angles instead of the degrees. One radian is approximately 57.3°.

   For a circle:

Arc Length = θ × r, (when θ is in radians)

Arc Length = (θ × π/180) × r, (when θ is in degrees)

Conclusion:

So here, we have discussed what we need to know about trapezoid and arc length. A trapezoid is a shape in mathematics or physics which has 4 sides. Two are parallel and two are perpendicular. Make sure to find out the height or altitude before finding out the angles. Don’t forget to label them

Arc length is used to find out the area under the curve around a circle. It includes two central angles. One is the central angle in degrees and the other is the central angle in radian. Make sure to check the correct formula for both of them.