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

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Example Question #11 : How To Find The Length Of The Side Of A Trapezoid

Isos. trap intermediate geo

Using the isosceles trapezoid shown above, find a possible base measurement for a similar trapezoid where the largest base measurement is .

Possible Answers:

Not enough information is provided.

Correct answer:

Explanation:

In order for two trapezoids to be similar their corresponding sides must have the same ratio. Since the largest base length in the image is and the corresponding side is , the other base must also be times greater than the corresponding side shown in the image.

The smaller base shown in the image has a length of , thus the corresponding side in the similar trapezoid must equal: $7\times3=21$ .

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Example Question #12 : How To Find The Length Of The Side Of A Trapezoid

Isos. trap intermediate geo

Using the image shown above, find the lenght for one of the two nonparallel equivalent sides for a similar trapezoid where the perimeter is equal to .

Possible Answers:

Correct answer:

Explanation:

In order for two trapezoids to be similar their corresponding sides must have the same ratio. Since the perimeter in the image is and the corresponding perimeter is , the corresponding sides must also be times greater than the corresponding sides shown in the image.

The nonparallel equivalent sides shown in the image have a length of , thus the corresponding side in the similar trapezoid must equal: $7\times2=14$ .

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Example Question #13 : How To Find The Length Of The Side Of A Trapezoid

Vt custom trap.

Using the trapezoid shown above, find the length of side .

Possible Answers:

$\sqrt{29}$

$2\sqrt{29}$

116

Correct answer:

$2\sqrt{29}$

Explanation:

In order to find the length of side , first note that the vertical side that has a length of and the base side with length must be perpendicular because they form a right angle. This means that the height of the trapezoid must equal . A right triangle can be formed on the interior of the trapezoid that has a height of and a base lenght of The base length can be derived by finding the difference between the two nonequivalent parallel bases.

Thus, the solution can be found by applying the formula: a^2+b^2=c^2 , where c=x.

4^2+10^2=c^2

16+100=c^2

116=c^2

$c=\sqrt{116}=\sqrt{4\times 29}=\sqrt{4}\sqrt{29}=2\sqrt{29}$

$x=2\sqrt{29}$

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Example Question #14 : How To Find The Length Of The Side Of A Trapezoid

An isosceles trapezoid has base measurements of $12\textup{ inches}$ and $4\textup{ inches}$ . The perimeter of the trapezoid is $28\textup{ inches}$ . Find the length for one of the two remaining sides.

Possible Answers:

$9\textup{ inches}$

$\frac{3}{4}\textup{ foot}$

$12\textup{ inches}$

$\frac{1}{2}\textup{ foot}$

$4\textup{ inches}$

Correct answer:

$\frac{1}{2}\textup{ foot}$

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.

Note: once you find the answer in inches, convert that quantity to an equivalent amount in feet.

Thus, the solution is:

28=12+4+2(leg)

28=16+2(leg)

2(leg)=28-16=12

$leg=\frac{12}{2}=6in.$

inch is equal to $\frac{1}{12}$ foot. Therefore, inches is equvalent to $\frac{1}{2}$ foot.

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Example Question #15 : How To Find The Length Of The Side Of A Trapezoid

Quadrilateral ABCD such that $\overline{AB} \parallel \overline{CD}$ , $\overline{AD} \nparallel \overline{BC}$ and $\overline{AD} \cong \overline{BC}$ . Which of the following correctly describes this quadrilateral?

Possible Answers:

Rectangle

Isosceles trapezoid

Kite

Rhombus

Non-isosceles trapezoid

Correct answer:

Isosceles trapezoid

Explanation:

Quadrilateral ABCD has at least one pair of parallel sides, $\overline{AB}$ and $\overline{CD}$ . The figure is, by definition, a parallelogram if and only if $\overline{AD} \parallel \overline{BC}$ , and, by definition, a trapezoid if and only if $\overline{AD} \nparallel \overline{BC}$ . Since $\overline{AD} \nparallel \overline{BC}$ , the figure is a trapezoid with bases $\overline{AB}$ and $\overline{CD}$ and legs $\overline{AD}$ and $\overline{BC}$ . Since $\overline{AD} \cong \overline{BC}$ , the trapezoid is by definition an isosceles trapezoid.

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

Study concepts, example questions & explanations for Intermediate Geometry

All Intermediate Geometry Resources

Example Questions

Example Question #11 : How To Find The Length Of The Side Of A Trapezoid

Example Question #12 : How To Find The Length Of The Side Of A Trapezoid

Example Question #13 : How To Find The Length Of The Side Of A Trapezoid

Example Question #14 : How To Find The Length Of The Side Of A Trapezoid

Example Question #15 : How To Find The Length Of The Side Of A Trapezoid

All Intermediate Geometry Resources

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