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Intermediate Geometry : How to find the perimeter of a trapezoid

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

Find the perimeter of the following trapezoid.

Geo_area2

Possible Answers:

$52\ ft$ $\displaystyle 52\ ft$

$50\ ft$ $\displaystyle 50\ ft$

$58\ ft$ $\displaystyle 58\ ft$

$74\ ft$ $\displaystyle 74\ ft$

$64\ ft$ $\displaystyle 64\ ft$

Correct answer:

$50\ ft$ $\displaystyle 50\ ft$

Explanation:

The answer is 50 ft. In order to find the perimeter, you must find the length of the left side. After some deduction $\displaystyle (19ft -13ft)$ , 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

$\displaystyle 8 + 13 + 10 + 19$

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

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

Trapezoid_measures

The height of a trapezoid is $\displaystyle 5$ cm and the length of $b_{1}$ $\displaystyle b_{1}$ is $\displaystyle 8$ cm.

Find the perimeter of the trapezoid to the nearest hundreth.

Possible Answers:

$\displaystyle 33.32 cm$

26 cm $\displaystyle 26 cm$

32 cm $\displaystyle 32 cm$

25.3 cm $\displaystyle 25.3 cm$

25 cm $\displaystyle 25 cm$

Correct answer:

$\displaystyle 33.32 cm$

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 $b_{2}$ $\displaystyle b_{2}$ :

$tan(60)=\frac{opposite}{adjacent}$ $\displaystyle tan(60)=\frac{opposite}{adjacent}$ . $Adjacent=\frac{5}{tan(60)}= 2.89$ $\displaystyle Adjacent=\frac{5}{tan(60)}= 2.89$ cm.

This finds the base of the triangle, which can be added twice to $b_{1}$ $\displaystyle b_{1}$ to find $b_{2}$ $\displaystyle b_{2}$ : $b_{2}=8+2.89+2.89=13.78$ $\displaystyle b_{2}=8+2.89+2.89=13.78$ cm.

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

$sin(60)=\frac{opposite}{hypotenuse}$ $\displaystyle sin(60)=\frac{opposite}{hypotenuse}$ . $Hypotenuse=\frac{5}{sin(60)}=5.77$ $\displaystyle Hypotenuse=\frac{5}{sin(60)}=5.77$ cm.

Lastly, add all of the lengths together: $b_{1}+b_{2}+2(l)=8+(2.78+2.78+8)+2(5.77)=33.32$ $\displaystyle b_{1}+b_{2}+2(l)=8+(2.78+2.78+8)+2(5.77)=33.32$ cm.

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

Find the perimeter of the trapezoid below.

Possible Answers:

210 $\displaystyle 210$

300 $\displaystyle 300$

234 $\displaystyle 234$

200 $\displaystyle 200$

214 $\displaystyle 214$

Correct answer:

200 $\displaystyle 200$

Explanation:

We can then use the Pythagorean Theorem to find the right portion of the bottom base. We can then use this value to determine the left portion.

Using Pythagorean Theorem again, we can calculate the left leg to be 20. That means we now know all four sides. The perimeter is simply the sum.

$\small P=20+52+34+94=200$ $\displaystyle \small P=20+52+34+94=200$

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

An isosceles trapezoid has two bases that are parallel to each other. The larger base is $\displaystyle 4$ times greater than the smaller base. The smaller base has a length of 2.5 $\displaystyle 2.5$ inches and the length of non-parallel sides of the trapezoid have a length of 4.5 $\displaystyle 4.5$ inches.

What is the perimeter of the trapezoid?

Possible Answers:

21.5in $\displaystyle 21.5in$

11.5in $\displaystyle 11.5in$

10.5in $\displaystyle 10.5in$

23in $\displaystyle 23in$

23.5in $\displaystyle 23.5in$

Correct answer:

21.5in $\displaystyle 21.5in$

Explanation:

To find the perimeter of this trapezoid, first find the length of the larger base. Then, find the sum of all of the sides. It's important to note that since this is an isosceles trapezoid, both of the non-parallel sides will have the same length.

The solution is:

The smaller base is equal to 2.5 $\displaystyle 2.5$ inches. Thus, the larger base is equal to:

$2.5\times4=10$ $\displaystyle 2.5\times4=10$

$\displaystyle Perimeter=base1+base2+(2S)$ , where $\displaystyle S=$ the length of one of the non-parallel sides of the isosceles trapezoid.

$P=2.5+10+(2\times 4.5)$ $\displaystyle P=2.5+10+(2\times 4.5)$

$\displaystyle P=2.5+10+9=21.5$

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

Dr. Robinson's property is shaped like an isosceles trapezoid. Dr. Robinson gave a contractor the following measurements, so that the contractor can build a wall around the enire property.

Measurements of property:

$\displaystyle base1: 15 yds$

$\displaystyle base2:7.5yds$

$\displaystyle non-parallel-sides: 8yds$

Find the perimeter of Dr. Robinson's property.

Possible Answers:

30.5 $\displaystyle 30.5$

42yds $\displaystyle 42yds$

28.5yds $\displaystyle 28.5yds$

38.5yds $\displaystyle 38.5yds$

28yds $\displaystyle 28yds$

Correct answer:

38.5yds $\displaystyle 38.5yds$

Explanation:

The measurements that Dr. Robinson gave to the contractor include the lengths of the two base sides and one of the non-parallel sides of the property. Since Dr. Robinson's property is shaped like an isosceles trapezoid, there must be two non-parallel sides of equal length.

The solution is:

$\displaystyle P=15+7.5+2(8)=15+7.5+16=38.5$

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Intermediate Geometry : How to find the perimeter of a trapezoid

Study concepts, example questions & explanations for Intermediate Geometry

All Intermediate Geometry Resources

Example Questions

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

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

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

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

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

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