Advanced Geometry : How to find the area of a trapezoid

Study concepts, example questions & explanations for Advanced Geometry

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Example Questions

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Example Question #1 : How To Find The Area Of A Trapezoid

Which of the following shapes is a trapezoid?

Shapes

Possible Answers:

Correct answer:

Explanation:

A trapezoid is a four-sided shape with straight sides that has a pair of opposite parallel sides. The other sides may or may not be parallel. A square and a rectangle are both considered trapezoids.

Example Question #2 : How To Find The Area Of A Trapezoid

What is the area of the following trapezoid?

Trapezoid

Possible Answers:

Correct answer:

Explanation:

The formula for the area of a trapezoid is:

,

where  is the value of the top base,  is value of the bottom base, and  is the value of the height.

Plugging in our values, we get:

Example Question #3 : How To Find The Area Of A Trapezoid

Screen_shot_2015-03-06_at_2.30.09_pm

What is the area of the trapezoid pictured above in square units?

Possible Answers:

Correct answer:

Explanation:

The formula for the area of a trapezoid is the average of the bases times the height,

 .

Looking at this problem and when the appropriate values are plugged in, the formula yields:

 

Example Question #4 : How To Find The Area Of A Trapezoid

Screen_shot_2015-03-06_at_2.44.49_pm

What is the height of the trapezoid pictured above?

Possible Answers:

Correct answer:

Explanation:

To find the height, we must introduce two variables, , each representing the bases of the triangles on the outside, so that . (Equation 1)

The next step is to set up two Pythagorean Theorems, 

 (Equation 2, 3)

The next step is a substitution from the first equation, 

 (Equation 4)

and plugging it in to the second equation, yielding 

 (Equation 5)

The next step is to substitute from Equation 3 into equation 5, 

 which simplifies to

Once we have one of the bases, just plug into the Pythagorean Theorem, 

Example Question #5 : How To Find The Area Of A Trapezoid

A isosceles trapezoid with sides , and  has a height of , what is the area?

Possible Answers:

Correct answer:

Explanation:

An isosceles trapezoid has two sides that are the same length and those are not the bases, so the bases are 10 and 20.

The area of the trapezoid then is:

Example Question #6 : How To Find The Area Of A Trapezoid

If the height of a trapezoid is , bottom base is , and the top base is , what is the area?

Possible Answers:

Correct answer:

Explanation:

The formula for finding the area of a trapezoid is:

Substitute the given values to find the area.

Example Question #7 : How To Find The Area Of A Trapezoid

Find the area of a trapezoid with bases of length  and  and a height of .

Possible Answers:

Correct answer:

Explanation:

The formula for the area of a trapezoid is:

Where  and  are the bases and  is the height. Using this formula and the given values, we get:

Example Question #8 : How To Find The Area Of A Trapezoid

Find the area of a trapezoid with bases of  and  and a height of .

Possible Answers:

Correct answer:

Explanation:

The formula for the area of a trapezoid is:

Where  and  are the bases and  is the height. Using this formula and the given values, we get:

Example Question #9 : How To Find The Area Of A Trapezoid

Trapezoid_1

Find the area of the above trapezoid.

Possible Answers:

Correct answer:

Explanation:

The formula for the area of a trapezoid is:

Where  and  are the bases and  is the height. Using this formula and the given values, we get:

Example Question #10 : How To Find The Area Of A Trapezoid

Trapezoid_2

Find the area of the above trapezoid.

Possible Answers:

Correct answer:

Explanation:

The formula for the area of a trapezoid is:

Where  and  are the bases and  is the height. Using this formula and the given values, we get:

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