Intermediate Geometry : Trapezoids

Study concepts, example questions & explanations for Intermediate Geometry

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Example Questions

Example Question #5 : How To Find An Angle In A Trapezoid

In the trapezoid below, find the degree measurement of .

5

Possible Answers:

Cannot be determined from the given information.

Correct answer:

Explanation:

In a trapezoid, the angles on the same leg (called adjacent angles) are supplementary, meaning they add up to  degrees.

 and the angle measuring  degrees are adjacent angles that are supplementary.

Example Question #6 : How To Find An Angle In A Trapezoid

In the trapezoid below, find the degree measurement of .

6

Possible Answers:

Cannot be determined from the information given.

Correct answer:

Explanation:

In a trapezoid, the angles on the same leg (called adjacent angles) are supplementary, meaning they add up to  degrees.

 and the angle measuring  degrees are adjacent angles that are supplementary.

Example Question #7 : How To Find An Angle In A Trapezoid

In the trapezoid below, find the degree measurement of .

7

Possible Answers:

Correct answer:

Explanation:

In a trapezoid, the angles on the same leg (called adjacent angles) are supplementary, meaning they add up to  degrees.

 and the angle measuring  degrees are adjacent angles that are supplementary.

Example Question #8 : How To Find An Angle In A Trapezoid

In the trapezoid below, find the degree measurement of .

8

Possible Answers:

Correct answer:

Explanation:

In a trapezoid, the angles on the same leg (called adjacent angles) are supplementary, meaning they add up to  degrees.

 and the angle measuring  degrees are adjacent angles that are supplementary.

Example Question #9 : How To Find An Angle In A Trapezoid

In the trapezoid below, find the degree measurement of .

9

Possible Answers:

Correct answer:

Explanation:

In a trapezoid, the angles on the same leg (called adjacent angles) are supplementary, meaning they add up to  degrees.

 and the angle measuring  degrees are adjacent angles that are supplementary.

Therefore, we can write the following equation and solve for a.

Example Question #10 : How To Find An Angle In A Trapezoid

In the trapezoid below, find the degree measurement of .

10

Possible Answers:

Correct answer:

Explanation:

In a trapezoid, the angles on the same leg (called adjacent angles) are supplementary, meaning they add up to  degrees.

 and the angle measuring  degrees are adjacent angles that are supplementary.

Therefore, we can write the following equation and solve for z.

Example Question #11 : How To Find An Angle In A Trapezoid

In the trapezoid below, find the degree measurement of .

11

Possible Answers:

Correct answer:

Explanation:

In a trapezoid, the angles on the same leg (called adjacent angles) are supplementary, meaning they add up to  degrees.

 and the angle measuring  degrees are adjacent angles that are supplementary.

Therefore, we can write the following equations and solve for y.

Example Question #12 : How To Find An Angle In A Trapezoid

In the trapezoid below, find the degree measurement of .

12

Possible Answers:

Correct answer:

Explanation:

In a trapezoid, the angles on the same leg (called adjacent angles) are supplementary, meaning they add up to  degrees.

 and the angle measuring  degrees are adjacent angles that are supplementary.

Thus, we can write the following equation and solve for x.

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

Find the perimeter of the following trapezoid. 

Geo_area2

Possible Answers:

Correct answer:

Explanation:

The answer is 50 ft.  In order to find the perimeter, you must find the length of the left side.  After some deduction , you can find that the base of the triangle is 6 ft.   Then using the Pythagorean Theorem, or 3-4-5 right triangles, you can find that the height of the triangle and rectangle is 8 ft. Geo_area2b

Once you find that the last side is 8 ft, you can add

 

to get an answer of 50 ft. for the perimeter. 

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

Trapezoid_measures

The height of a trapezoid is  cm and the length of  is  cm.

Find the perimeter of the trapezoid to the nearest hundreth.

Possible Answers:

Correct answer:

Explanation:

Use the triangle formed by the height of the trapezoid to find the lengths of the two sides of the trapezoid and the length of :

 .   cm.

This finds the base of the triangle, which can be added twice to  to find  cm.

Now, use the same triangle to find the length of the sides.

 .  cm.

Lastly, add all of the lengths together:  cm.

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