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

Example Questions

Example Question #31 : Quadrilaterals

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 #261 : Geometry

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

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 #271 : Isee Upper Level (Grades 9 12) Mathematics Achievement

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 #272 : Isee Upper Level (Grades 9 12) Mathematics Achievement

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.

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 #273 : Isee Upper Level (Grades 9 12) Mathematics Achievement

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: