Perimeter of a Trapezoid - Examples, Exercises and Solutions

The trapezoid is a quadrilateral defined as having 2 parallel opposite sides. The calculation of the perimeter of the trapezoid is solved using a very simple formula that we will see below: all sides are added together. This type of questions can appear in tests of the first and second level in the first years of high school and also in final exams of level 3, 4 and 5 for the graduation of the secondary cycle.

Suggested Topics to Practice in Advance

  1. Area
  2. Trapezoids

Practice Perimeter of a Trapezoid

Exercise #1

What is the perimeter of the trapezoid in the figure?

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Video Solution

Step-by-Step Solution

To find the perimeter we will add all the sides:

4+5+9+6=9+9+6=18+6=24 4+5+9+6=9+9+6=18+6=24

Answer

24

Exercise #2

Look at the trapezoid in the figure.

The long base is 1.5 times longer than the short base.

Find the perimeter of the trapezoid.

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Video Solution

Step-by-Step Solution

First, we calculate the long base from the existing data:

Multiply the short base by 1.5:

5×1.5=7.5 5\times1.5=7.5

Now we will add up all the sides to find the perimeter:

2+5+3+7.5=7+3+7.5=10+7.5=17.5 2+5+3+7.5=7+3+7.5=10+7.5=17.5

Answer

17.5

Exercise #3

The perimeter of the trapezoid in the diagram is 25 cm. Calculate the missing side.

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Video Solution

Step-by-Step Solution

We replace the data in the formula to find the perimeter:

25=4+7+11+x 25=4+7+11+x

25=22+x 25=22+x

2522=x 25-22=x

3=x 3=x

Answer

3 3 cm

Exercise #4

Shown below is the isosceles trapezoid ABCD.

Given in cm:
BC = 7  

Height of the trapezoid (h) = 5

Perimeter of the trapezoid (P) = 34

Calculate the area of the trapezoid.

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Video Solution

Step-by-Step Solution

Since ABCD is a trapezoid, it can be argued that:

AD=BC=7 AD=BC=7

The formula to find the area will be

SABCD=(AB+DC)×h2 S_{ABCD}=\frac{(AB+DC)\times h}{2}

Since we are given the perimeter of the trapezoid, we can findAB+DC AB+DC

PABCD=7+AB+7+DC P_{ABCD}=7+AB+7+DC

34=14+AB+DC 34=14+AB+DC

3414=AB+DC 34-14=AB+DC

20=AB+DC 20=AB+DC

Now we will place the data we received in the formula to calculate the area of the trapezoid:

S=20×52=1002=50 S=\frac{20\times5}{2}=\frac{100}{2}=50

Answer

50

Exercise #5

ABCD is an isosceles trapezoid.

AB = 3

CD = 6

The area of the trapezoid is 9 cm².

What is the perimeter of the trapezoid?

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Video Solution

Step-by-Step Solution

We will find the height BE by calculating the trapezoidal area formula:

S=(AB+CD)2×h S=\frac{(AB+CD)}{2}\times h

We replace the known data: 9=(3+6)2×BE 9=\frac{(3+6)}{2}\times BE

We multiply by 2 to get rid of the fraction:

9×2=9×BE 9\times2=9\times BE

18=9BE 18=9BE

We divide the two sections by 9:

189=9BE9 \frac{18}{9}=\frac{9BE}{9}

2=BE 2=BE

If we draw the height from A to CD we get a rectangle and two congruent triangles. That is:

AF=BE=2 AF=BE=2

AB=FE=3 AB=FE=3

ED=CF=1.5 ED=CF=1.5

Now we will find one of the legs through the Pythagorean theorem.

We focus on triangle BED:

BE2+ED2=BD2 BE^2+ED^2=BD^2

We replace the known data:

22+1.52=BD2 2^2+1.5^2=BD^2

4+2.25=DB2 4+2.25=DB^2

6.25=DB2 6.25=DB^2

We extract the root:

6.25=DB \sqrt{6.25}=DB

2.5=DB 2.5=DB

Now that we have found DB, it can be argued that:

AC=BD=2.5 AC=BD=2.5

We calculate the perimeter of the trapezoid:6+3+2.5+2.5= 6+3+2.5+2.5=

9+5=14 9+5=14

Answer

14

Exercise #1

ABC is an isosceles triangle.

AD is the height of triangle ABC.

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AF = 5

AB = 17
AG = 3

AD = 8

What is the perimeter of the trapezoid EFBC?

Video Solution

Step-by-Step Solution

To find the perimeter of the trapezoid, all its sides must be added:

We will focus on finding the bases.

To find GF we use the Pythagorean theorem: A2+B2=C2 A^2+B^2=C^2 in the triangle AFG

We replace

32+GF2=52 3^2+GF^2=5^2

We isolate GF and solve:

9+GF2=25 9+GF^2=25

GF2=259=16 GF^2=25-9=16

GF=4 GF=4

We perform the same process with the side DB of the triangle ABD:

82+DB2=172 8^2+DB^2=17^2

64+DB2=289 64+DB^2=289

DB2=28964=225 DB^2=289-64=225

DB=15 DB=15

We start by finding FB:

FB=ABAF=175=12 FB=AB-AF=17-5=12

Now we reveal EF and CB:

GF=GE=4 GF=GE=4

DB=DC=15 DB=DC=15

This is because in an isosceles triangle, the height divides the base into two equal parts so:

EF=GF×2=4×2=8 EF=GF\times2=4\times2=8

CB=DB×2=15×2=30 CB=DB\times2=15\times2=30

All that's left is to calculate:

30+8+12×2=30+8+24=62 30+8+12\times2=30+8+24=62

Answer

62

Exercise #2

What can be said about the two trapezoids in the diagram?

x+517y10x12

Video Solution

Step-by-Step Solution

We calculate the perimeter of the left trapezoid:

P=10+12+x+y P=10+12+x+y

P=22+x+y P=22+x+y

We calculate the perimeterof the right trapezoid:

P=x+5+17+y3+2y3 P=x+5+17+\frac{y}{3}+\frac{2y}{3}

P=x+22+2y+y3 P=x+22+\frac{2y+y}{3}

P=x+22+3y3 P=x+22+\frac{3y}{3}

P=x+22+y P=x+22+y

It can be seen that the two perimeters are identical to each other.

Answer

Their perimeters are identical.

Exercise #3

Given the trapezoids in the drawing.

Are they the same trapezoid?

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Video Solution

Step-by-Step Solution

We calculate the perimeter of the left trapezoid:

P=6+10+7+52x+5 P=6+10+7+\frac{5}{2}x+5

P=28+52x P=28+\frac{5}{2}x

We calculate the perimeter of the right trapezoid:

P=7+x+x+16+x2+5 P=7+x+x+16+\frac{x}{2}+5

P=212x+28 P=2\frac{1}{2}x+28

P=52x+28 P=\frac{5}{2}x+28

The perimeters of the two trapezoids are equal to each other.

Answer

No, but their perimeter is identical.

Exercise #4

Calculate the perimeter of the trapezoid according to the following data:

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Video Solution

Answer

36

Exercise #5

Look at the trapezoid in the figure.

Calculate its perimeter.

2.52.52.510.410.410.45.35.35.3666

Video Solution

Answer

24.2

Exercise #1

What is the perimeter of the trapezoid in the figure?

7.57.57.54441.51.51.5333

Video Solution

Answer

16

Exercise #2

AB = 5

CD = 7

AC = 4

BD = 4

Calculate the perimeter of the rectangle.

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Video Solution

Answer

20

Exercise #3

AB = 10.5

CD = 13

AC = 7.5

BD = 7.5

Calculate the perimeter of the rectangle ABCD.

10.510.510.57.57.57.51313137.57.57.5AAABBBDDDCCC

Video Solution

Answer

38.5

Exercise #4

Given the trapezoid:

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What is its perimeter?

Video Solution

Answer

32

Exercise #5

Look at the trapezoid in the diagram.

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What is its perimeter?

Video Solution

Answer

36

Topics learned in later sections

  1. Perimeter