ISEE Upper Level Math : How to find the area of a trapezoid

Study concepts, example questions & explanations for ISEE Upper Level Math

varsity tutors app store varsity tutors android store

Example Questions

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

Trapezoid

Note: Figure NOT drawn to scale.

The above trapezoid has area . What is  ?

Possible Answers:

Correct answer:

Explanation:

Substitute  in the formula for the area of a trapezoid:

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

A trapezoid has height 20 inches. Its bases have sum 30 inches, and one base is 6 inches longer than the other. What is the area of this trapezoid?

Possible Answers:

It cannot be determined from the information given.

Correct answer:

Explanation:

You do not need to find the individual bases; their sum, , is . You can substitute  into the formula for the area of a trapezoid:

 square inches.

Note that the fact that one base is  inches longer is not important here.

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

Trapezoidr

 

Find the area of the above trapezoid if , , and .

Figure not drawn to scale.

Possible Answers:

Correct answer:

Explanation:

The area of a trapezoid is given by

,

 where  are the lengths of each base and is the altitude (height) of the trapezoid. 

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

A trapezoid has the base lengths of and . The area of the trapezoid is . Give the height of the trapezoid in terms of .

Possible Answers:

Correct answer:

Explanation:

The area of a trapezoid is given by

,

where  are the lengths of each base and is the altitude (height) of the trapezoid.

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

In the following trapezoid  and . The area of the trapezoid is 54 square inches. Give the height of the trapezoid. Figure not drawn to scale.

Trap

Possible Answers:

Correct answer:

Explanation:

The area of a trapezoid is given by

,

where  are the lengths of each base and is the altitude (height) of the trapezoid. 

Substitute these values into the area formula:

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

Square 3

What is the area of the shaded portion of the above square?

Possible Answers:

Correct answer:

Explanation:

Quadrilateral  - the shaded region - is a trapezoid with bases  and , and altitude . The area of the trapezoid can be calculated using the formula 

,

where  and  , and .

The length of  can be found by setting  and  and applying the Pythagorean Theorem:

Therefore, 

.

Substituting:

 

Learning Tools by Varsity Tutors

Incompatible Browser

Please upgrade or download one of the following browsers to use Instant Tutoring: