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Word Problems: Area and Perimeter of Trapezoids
In order to solve problems which require application of the area and perimeter for trapezoids, it is necessary to
 
 
In a typical problem involving area and perimeter of a trapezoid, we are given some measurements of the bases, height, area, or perimeter and asked to calculate the others. The problem can be easier if we know that the trapezoid is isosceles (the non-parallel sides are of equal length).
 
Suppose in a trapezoid the bases are 8 and 5 and the height is 4. What are the area and perimeter of this trapezoid?
 
Two diagrams that illustrate these given are shown below. Notice that s1> s2 and that symmetry is not a condition of the trapezoid. Unfortunately, we could construct infinitely many trapezoids with bases of 8 and 5 and a height of 4.
 
 
Although we can NOT find the perimeter because the possible trapezoids which we can draw can have different lengths for the other two sides, we can, interestingly enough, find the area of any trapezoid meeting the base and height requirements by using the formula
 
A = (½ h)(B + b)
A = (2)(13)
A = 26
 
Notice the importance of making a diagram (or more than one) to see what is happening when using the given information.

Let's Practice

Question #1
Audio
A diagram of a trapezoid with measured segments is shown below. What are the area and perimeter of this trapezoid?


Question #2
Audio
A trapezoid is shown in the diagram below. What are its area and perimeter?



Try These
Question #1
Audio
A trapezoid is shown in the diagram below. What are its area and perimeter?


Question #2
Audio
An isosceles trapezoid is shown in the diagram below. What are the area and perimeter of this trapezoid?



This type of problem involves relationships among the lengths of the sides and height as well as the area, and perimeter of a trapezoid. Since the height is perpendicular to both parallel bases, it is often possible to form a right triangle and use the Pythagorean Theorem to calculate missing measurements. Remember that sometimes there is not enough information given to find the perimeter. While the bases and height do determine the area, there are infinitely many trapezoids with the same bases and height, but different non-parallel sides.

M Ransom

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