Trapezoid area - Examples, Exercises and Solutions

To find the area of a trapezoid, you need the following three pieces of information:

  • The length of base one
  • The length of base two
  • The height between the two bases

The formula to find the area of a trapezoid is as follows:

The sum of the bases multiplied by the height and then divided by two.

Formula of the trapezoid:

A=(Base 1+Base 2)×Height2 A=\frac{(Base~1+Base~2)\times Height}{2}

A1 - How do you calculate the area of a new trapezoid

Practice Trapezoid area

examples with solutions for trapezoid area

Exercise #1

The trapezoid ABCD is shown below.

AB = 2.5 cm

DC = 4 cm

Height (h) = 6 cm

Calculate the area of the trapezoid.

2.52.52.5444h=6h=6h=6AAABBBCCCDDD

Video Solution

Step-by-Step Solution

First, let's remind ourselves of the formula for the area of a trapezoid:

A=(Base + Base) h2 A=\frac{\left(Base\text{ }+\text{ Base}\right)\text{ h}}{2}

We substitute the given values into the formula:

(2.5+4)*6 =
6.5*6=
39/2 = 
19.5

Answer

1912 19\frac{1}{2}

Exercise #2

Given the trapezoid:

999121212555AAABBBCCCDDDEEE

What is the area?

Video Solution

Step-by-Step Solution

Formula for the area of a trapezoid:

(base+base)2×altura \frac{(base+base)}{2}\times altura

We substitute the data into the formula and solve:

9+122×5=212×5=1052=52.5 \frac{9+12}{2}\times5=\frac{21}{2}\times5=\frac{105}{2}=52.5

Answer

52.5

Exercise #3

Calculate the area of the trapezoid.

555141414666

Video Solution

Step-by-Step Solution

We use the formula (base+base) multiplied by the height and divided by 2.

Note that we are only provided with one base and it is not possible to determine the size of the other base.

Therefore, the area cannot be calculated.

Answer

Cannot be calculated.

Exercise #4

What is the area of the trapezoid in the figure?

777151515222AAABBBCCCDDDEEE

Video Solution

Step-by-Step Solution

We use the formula to calculate the area of a trapezoid: (base+base) multiplied by the height divided by 2:

(AB+DC)×BE2 \frac{(AB+DC)\times BE}{2}

(7+15)×22=22×22=442=22 \frac{(7+15)\times2}{2}=\frac{22\times2}{2}=\frac{44}{2}=22

Answer

22 22 cm².

Exercise #5

What is the area of the trapezoid in the figure?

222999777AAABBBCCCDDD

Video Solution

Step-by-Step Solution

We use the formula: (base + base) multiplied by height divided by 2:

S=(AB+DC)×h2 S=\frac{(AB+DC)\times h}{2}

Keep in mind that AD is the height of a trapezoid:

We replace the existing data in the formula:

S=(2+9)×72 S=\frac{(2+9)\times7}{2}

S=11×72=772=38.5 S=\frac{11\times7}{2}=\frac{77}{2}=38.5

Answer

38.5 38.5 cm².

examples with solutions for trapezoid area

Exercise #1

Given the trapezoid in front of you:

AAABBBCCCDDD151269

Given h=9, DC=15.

Since the area of the trapezoid ABCD is equal to 126.

Find the length of the side AB.

Video Solution

Step-by-Step Solution

We use the formula to calculate the area: (base+base) times the height divided by 2

S=(AB+CD)×h2 S=\frac{(AB+CD)\times h}{2}

We input the data we are given:

126=(AB+15)×92 126=\frac{(AB+15)\times9}{2}

We multiply the equation by 2:

252=9AB+135 252=9AB+135

252135=9AB 252-135=9AB

117=9AB 117=9AB

We divide the two sections by 9

13=AB 13=AB

Answer

13

Exercise #2

The trapezoid ABCD is shown below.

AB = 4 cm

DC = 8 cm

Area of the trapezoid (S) = 30 cm²

Calculate the height of the trapezoid.

S=30S=30S=30444888AAABBBCCCDDD

Video Solution

Step-by-Step Solution

We use the formula to calculate the area: (base+base) times the height divided by 2

We replace the existing data:

S=(AB+CD)×h2 S=\frac{(AB+CD)\times h}{2}

30=(4+8)×h2 30=\frac{(4+8)\times h}{2}

We multiply the equation by 2:

60=(4+8)h 60=(4+8)h

60=12h 60=12h

We divide the two sections by 12:

6012=h \frac{60}{12}=h

5=h 5=h

Answer

5

Exercise #3

Given the trapezoid:

S=30S=30S=30666999AAABBBCCCDDDEEE

What is the height?

Video Solution

Step-by-Step Solution

Formula for the area of a trapezoid:

(base+base)2×altura \frac{(base+base)}{2}\times altura

We substitute the data into the formula

9+62×h=30 \frac{9+6}{2}\times h=30

We solve:

152×h=30 \frac{15}{2}\times h=30

712×h=30 7\frac{1}{2}\times h=30

h=30712 h=\frac{30}{7\frac{1}{2}}

h=4 h=4

Answer

4

Exercise #4

The area of the trapezoid in the diagram is 1.375 cm².

Work out the length of the side marked in red.

4440.50.50.5AAABBBCCCDDD

Video Solution

Step-by-Step Solution

The area of the trapezoids will be equal to: S=(AB+DC)2×h S=\frac{(AB+DC)}{2}\times h

We replace the data we have in the formula:

1.375=AB+42×0.5 1.375=\frac{AB+4}{2}\times0.5

We multiply by 2 to get rid of the fraction:

2.75=(AB+4)×12 2.75=(AB+4)\times\frac{1}{2}

We multiply by 2:

5.5=AB+4 5.5=AB+4

5.54=AB 5.5-4=AB

1.5=AB 1.5=AB

Answer

1.5 1.5 cm

Exercise #5

Given the following trapezoid:

AAABBBCCCDDD57

Find the area of the trapezoid ABCD.

Video Solution

Step-by-Step Solution

The area of the trapezoid will be:

S=(AB+DC)×h2 S=\frac{(AB+DC)\times h}{2}

We replace the known data in the formula:

(5+7)2×83= \frac{(5+7)}{2}\times\frac{8}{3}=

12×86= \frac{12\times8}{6}=

966=16 \frac{96}{6}=16

Answer

16

examples with solutions for trapezoid area

Exercise #1

ABCD is a trapezoid.

AB = 4 cm

DC = 7 cm

BK = 6 cm

Can the trapezoidal area formula be applied? If so, apply it and calculate.

444777666AAABBBCCCDDDKKK

Video Solution

Step-by-Step Solution

The formula for the area of a trapezoid is:

S=(AB+DC)×h2 S=\frac{(AB+DC)\times h}{2}

Since we are given AB and DC but not the height, we cannot calculate the area of the trapezoid.

Answer

It cannot be applied.

Exercise #2

Look at the trapezoid in the figure.

Its area is equal to 35 cm².

Calculate its perimeter.

6665.55.55.5888AAABBBCCCDDD

Video Solution

Step-by-Step Solution

We use the formula to find the area of a trapezoid and replace the existing data in it:

S=(AB+CD)×h2 S=\frac{(AB+CD)\times h}{2}

We recognize that AD is the height of the trapezoid

35=(6+8)×AD2 35=\frac{(6+8)\times AD}{2}

35=142AD 35=\frac{14}{2}AD

35=7AD 35=7AD

We divide the two sections by 7:

5=AD 5=AD

Now we calculate the perimeter by adding all the sides:

5+6+8+5.5=11+8+5.5=19+5.5=24.5 5+6+8+5.5=11+8+5.5=19+5.5=24.5

Answer

24.5 24.5 cm

Exercise #3

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.

777h=5h=5h=5AAABBBCCCDDDEEE

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 #4

Below is an equilateral hexagon.

AB = 7
FC = 14
AE = 12.124

77712.12412.12412.124141414AAABBBCCCDDDEEEFFFGGG

What is the area of the hexagon?

Video Solution

Step-by-Step Solution

The hexagon consists of two equal trapezoids, so we will strive to calculate the area of one of them and multiply it.

AFE is an isosceles triangle,

its height (FG) crosses the base exactly in the center, therefore:

AG=GE AG=GE

AG=12AE AG=\frac{1}{2}AE

We replace and discover:

AE=12×12=6 AE=\frac{1}{2}\times12=6

We replace the data in the formula for the area of a trapezoid:

(base+base)2×altura \frac{(base+base)}{2}\times altura

7+142×6=212×6=10.5×6=63 \frac{7+14}{2}\times6=\frac{21}{2}\times6=10.5\times6=63

63 is the area of half of the hexagon, therefore:

63×2=126 63\times2=126

Answer

127.3

Exercise #5

The trapezoid DECB forms part of triangle ABC.

AB = 6 cm
AC = 10 cm

Calculate the area of the trapezoid DECB, given that DE divides both AB and AC in half.

666101010AAABBBCCCDDDEEE


Video Solution

Step-by-Step Solution

DE crosses AB and AC, that is to say:

AD=DB=12AB=12×6=3 AD=DB=\frac{1}{2}AB=\frac{1}{2}\times6=3

AE=EC=12AC=12×10=5 AE=EC=\frac{1}{2}AC=\frac{1}{2}\times10=5

Now let's look at triangle ADE, two sides of which we have already calculated.

Now we can find the third side DE using the Pythagorean theorem:

AD2+DE2=AE2 AD^2+DE^2=AE^2

We substitute our values into the formula:

32+DE2=52 3^2+DE^2=5^2

9+DE2=25 9+DE^2=25

DE2=259 DE^2=25-9

DE2=16 DE^2=16

We extract the root:

DE=16=4 DE=\sqrt{16}=4

Now let's look at triangle ABC, two sides of which we have already calculated.

Now we can find the third side (BC) using the Pythagorean theorem:

AB2+BC2=AC2 AB^2+BC^2=AC^2

We substitute our values into the formula:

62+BC2=102 6^2+BC^2=10^2

36+BC2=100 36+BC^2=100

BC2=10036 BC^2=100-36

BC2=64 BC^2=64

We extract the root:

BC=64=8 BC=\sqrt{64}=8

Now we have all the data needed to calculate the area of the trapezoid DECB using the formula:

(base + base) multiplied by the height divided by 2:

Keep in mind that the height in the trapezoid is DB.

S=(4+8)2×3 S=\frac{(4+8)}{2}\times3

S=12×32=362=18 S=\frac{12\times3}{2}=\frac{36}{2}=18

Answer

18

Topics learned in later sections

  1. Area
  2. Trapezoids
  3. Perimeter of a trapezoid
  4. Perimeter