# Intermediate Geometry : How to find the length of the side of a trapezoid

## Example Questions

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

Suppose the area of the trapezoid is , with a height of  and a base of .  What must be the length of the other base?

Explanation:

Write the formula for finding the area of a trapezoid.

Substitute the givens and solve for either base.

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

If the area of a trapezoid is , the height of the trapezoid is , and the base length is , what must be the length of the other base?

Explanation:

Write the formula for the area of a trapezoid.

Substitute all the given values and solve for the base.

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

An isosceles trapezoid has base measurements of  and . The perimeter of the trapezoid is . Find the length for one of the two remaining sides.

Explanation:

To solve this problem, first note that an isosceles trapezoid has two parallel bases that are nonequivalent in length. Additionally, an isosceles trapezoid must have two nonparallel sides that have equivalent lengths. Since this problem provides the length for both of the bases as well as the total perimeter, the missing sides can be found using the following formula: Perimeter= Base one  Base two  (leg), where the length of "leg" is one of the two equivalent nonparallel sides.

Thus, the solution is:

Check the solution by plugging in the answer:

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

An isosceles trapezoid has base measurements of  and . Additionally, the isosceles trapezoid has a height of . Find the length for one of the two missing sides.

Explanation:

In order to solve this problem, first note that an isosceles trapezoid has two parallel bases that are nonequivalent in length. Additionally, an isosceles trapezoid must have two nonparallel sides that have equivalent lengths.

This problem provides the lengths for each of the bases as well as the height of the isosceles trapezoid. In order to find the length for one of the two equivalent nonparallel legs of the trapezoid, first use the height of the trapezoid to form right triangles on the interior of the trapezoid that each have a base length of . See image below:

Note: the base length of  can be found by subtracting the lengths of the two bases, then dividing that difference in half:

Now, apply the formula , where  the length for one of the two equivalent nonparallel legs of the trapezoid.

Thus, the solution is:

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

The isosceles trapezoid shown above has base measurements of  and . Additionally, the trapezoid has a height of . Find the length of side

Explanation:

In this problem the lengths for each of the bases and the height of the isosceles trapezoid is provided in the question prompt. In order to find the length for one of the two equivalent nonparallel legs of the trapezoid (side ), first use the height of the trapezoid to form right triangles on the interior of the trapezoid that each have a base length of .

The base of the interior triangles is equal to  because the difference between the two bases is equal to . And, this difference must be divided evenly in half because the isosceles trapezoid is symmetric--due to the two equivalent nonparallel sides and the two nonequivalent parallel bases.

Now, apply the pythagorean theorem: , where .

Thus,

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

Using the isosceles trapezoid shown above, find the length for one of the two nonparallel equivalent sides.

Explanation:

To solve this problem, first note that an isosceles trapezoid has two parallel bases that are nonequivalent in length. Additionally, an isosceles trapezoid must have two nonparallel sides that have equivalent lengths. Since this problem provides the length for both of the bases as well as the total perimeter, the missing sides can be found using the following formula: Perimeter= Base one  Base two  (leg), where the length of "leg" is one of the two equivalent nonparallel sides.

Thus, the solution is:

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

An isosceles trapezoid has one base measurement of  and the length for one of the nonparallel sides is . The perimeter of the trapezoid is . Find the length for the other base of the trapezoid.

Not enough information is provided in this problem.

Explanation:

To solve this problem, first note that an isosceles trapezoid has two parallel bases that are nonequivalent in length. Additionally, an isosceles trapezoid must have two nonparallel sides that have equivalent lengths.

Therefore, use the given information to apply the formula:

Perimeter= Base one  Base two  (leg), where the length of "leg" is one of the two equivalent nonparallel sides.

Thus, the solution is:

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

An isosceles trapezoid has base measurements of  and , respectively. Additionally, the isosceles trapezoid has a height that is  the measurement of the larger base. Find the length for one of the two equivalent nonparallel sides.

Explanation:

In order to solve this problem, first note that an isosceles trapezoid has two parallel bases that are nonequivalent in length. Additionally, an isosceles trapezoid must have two nonparallel sides that have equivalent lengths.

This problem provides the lengths for each of the bases as well as informataion regarding the height of the isosceles trapezoid. In order to find the length for one of the two equivalent nonparallel legs of the trapezoid, use the height of the trapezoid to form right triangles on the interior of the trapezoid that each have a base length of . The interior triangle base length of  can be found by subtracting the lengths of the two bases, then dividing that difference in half:

In order to calculate the exact height of the isosceles trapezoid (as well as the interior triangle), find  of the larger base. Since the largest base of the trapezoid is , the height of the trapezoid is:

Now you have enough information to apply the formula , where  one of the missing sides.

The final solution is:

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

An isosceles trapezoid has base measurements of  and . The perimeter of the trapezoid is . Find the length for one of the two remaining sides.

Explanation:

To solve this problem, first note that an isosceles trapezoid has two parallel bases that are nonequivalent in length. Additionally, an isosceles trapezoid must have two nonparallel sides that have equivalent lengths. Since this problem provides the length for both of the bases as well as the total perimeter, the missing sides can be found using the following formula: Perimeter= Base one  Base two  (leg), where the length of "leg" is one of the two equivalent nonparallel sides.

Thus, the solution is:

Check the solution by plugging in the answer:

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

An isosceles trapezoid has one base measurement of  and the length for one of the nonparallel sides is . The perimeter of the trapezoid is . Find the length for the other base of the trapezoid.

Explanation:

To solve this problem, first note that an isosceles trapezoid has two parallel bases that are nonequivalent in length. Additionally, an isosceles trapezoid must have two nonparallel sides that have equivalent lengths.

Therefore, use the given information to apply the formula:

Perimeter= Base one  Base two  (leg), where the length of "leg" is one of the two equivalent nonparallel sides.

Thus, the solution is:

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