Calculating the Area of a Trapezoid

Finally we will look at a few example computations of the area for a few trapezoids. The solution for finding the area is shown for the first example below. The shaded trapezoid on the velocity-time graph has a base of 2 seconds and heights of 10 m/s (on the left side) and 30 m/s (on the right side). Since the area of trapezoid is found by using the formula A = ½ * (b) * (h1 + h2), the area is 40 m [½ * (2 s) * (10 m/s + 30 m/s)]. That is, the object was displaced 40 meters during the time interval from 1 second to 3 seconds.

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Area = ½ * b * (h1 + h2)
Area = ½ * (2 s) * (10 m/s + 30 m/s)

Area = 40 m





http://www.physicsclassroom.com/Class/images/qwikquiz.webpNow try the following two practice problems as a check of your understanding. Determine the displacement of the object during the time interval from 2 to 3 seconds (Practice A) and during the first 2 seconds (Practice B).

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Quick Quiz Answer

The area of a trapezoid is given by the formula

Area = ½ • b • (h1 + h2) where b = 1 s and h1 = 20 m/s and h2 = 30 m/s.

Area = ½ • (1 s) • (20 m/s + 30 m/s) = 25 m

That is, the object was displaced 25 m during the time interval from 2 to 3 wseconds.

 

 
Check your understanding answer

The area of a trapezoid is given by the formula

Area = ½ • b • (h1 + h2) where b = 2 s and h1 = 30 m/s and h2 = 10 m/s

Area = ½ • (2 s) • (30 m/s + 10 m/s) = 40 m

That is, the object was displaced 40 m during the time interval from 2 to 3 seconds.