What is the Formula for Area of Trapezoid?

What is the area of the above trapezoid?

Possible Answers:

Correct answer:

Explanation:

To find the area of a trapezoid, multiply one half (or 0.5, since we are working with decimals) by the sum of the lengths of its bases (the parallel sides) by its height (the perpendicular distance between the bases). This quantity is

Find the area of the trapezoid:

Possible Answers:

Correct answer:

Explanation:

The area of a trapezoid can be determined using the equation

.

What is the area of the trapezoid?

Possible Answers:

Correct answer:

Explanation:

To find the area of a trapezoid, multiply the sum of the bases (the parallel sides) by the height (the perpendicular distance between the bases), and then divide by 2.

The above diagram depicts a rectangle

 with isosceles triangle
. If
 is the midpoint of
, and the area of the orange region is
, then what is the length of one leg of
 ?

Possible Answers:

Correct answer:

Explanation:

The length of a leg of

 is equal to the height of the orange region, which is a trapezoid. Call this length/height
.

Since the triangle is isosceles, then

, and since
 is the midpoint of
,
. Also, since opposite sides of a rectangle are congruent, 

Therefore, the orange region is a trapezoid with bases 

and
 and height
. Its area is 72, so we can set up and solve this equation using the area formula for a trapezoid:

 

This is the length of one leg of the triangle.

A trapezoid has a height of

 inches and bases measuring
 inches and
 inches. What is its area?

Possible Answers:

Correct answer:

Explanation:

Use the following formula, with 

:

Find the area of a trapezoid with bases equal to 7 and 9 and height is 2.

Possible Answers:

Correct answer:

Explanation:

To solve, simply use the formula for the area of a trapezoid.

Thus,

Find the area of a trapezoid with bases of 10 centimeters and 8 centimeters, and a height of 4 centimeters.

Possible Answers:

Correct answer:

Explanation:

The formula for area of a trapezoid is:

 where

therefore the area equation becomes,

You recently bought a new bookshelf with a base in  the shape of an isosceles trapezoid. If the small base is 2 feet, the large base is 3 feet, and the depth is 8 inches, what is the area of the base of your new bookshelf?

Possible Answers:

Cannot be determined from the information provided.

Correct answer:

Explanation:

You recently bought a new bookshelf with a base in  the shape of an isosceles trapezoid. If the small base is 2 feet, the large base is 3 feet, and the depth is 8 inches, what is the area of the base of your new bookshelf?

To find the area of a trapezoid, we need to use the following formula:

Where a and b are the lengths of the bases, and h is the perpendicular distance from one base to another.

We are given a and b, and then h will be the same as our depth. The tricky part is realizing that our depth is in inches, while our base lengths are in feet. We need to convert 8 inches to feet:

Next, plug it all into our equation up above.

So our answer is:

The above diagram shows Rectangle 

, with midpoint 
 of 
.

The area of Quadrilateral 

 is . Evaluate 
.

Possible Answers:

Correct answer:

Explanation:

The easiest way to see this problem is to note that Quadrilateral 

 has as its area that of Rectangle 
 minus that of 
.

The area of Rectangle 

 is its length multiplied by its width:

 is the midpoint of 
, so 
 has as its base and height 
 and 
, respectively; 

its area is half their product, or 

The area of  Quadrilateral 

 is 

, so

Omar
Certified Tutor

Arizona State University, Bachelors, Civil Engineering.

Andrew
Certified Tutor

University of South Florida-Main Campus, Bachelors, Biomedical Sciences. New York Medical College, PHD, Doctor of Medicine.

Mike
Certified Tutor

Concordia University-Ann Arbor, Master of Arts Teaching, Mathematics Teacher Education.

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