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

Know how to use basic formulas for area and perimeter of a trapezoid. The area is (½ h)(B + b) where B and b are the lengths of the two parallel bases and h is the height (perpendicular distance between parallel bases). The perimeter is found by adding the lengths of the four sides.
Use the Pythagorean Theorem in finding the side(s) of a right triangle.

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

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

Question #2

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

Try These


Question #1
		A trapezoid is shown in the diagram below. What are its area and perimeter?
	A. area = 46 and the perimeter cannot be found.
	B. area = 138 and the perimeter = 40
	C. area = 46 and the perimeter =32

Question #2

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

A. perimeter = and area = 90
B. perimeter = and area = 90
C. perimeter = and area = 90.