Area of a Trapezoid: Calculate The Missing Side based on the formula

Finding Area based off Perimeter and Vice VersaSubtraction or addition to a larger shapeSuggesting options for terms when the formula result is knownUsing Pythagoras' theoremUsing ratios for calculationUsing variablesUsing additional geometric shapesApplying the formula
Question 1

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

Question 2

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.

Question 3

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

Question 4

Given the trapezoid:

S=30S=30S=30666999AAABBBCCCDDDEEE

What is the height?

Question 5

The area of trapezoid ABCD is equal to 45 cm².

The base of the trapezoid BC is equal to 4 cm.

The base of the trapezoid AD is equal to 6 cm.

Calculate the length of AE.

S=45S=45S=45444666AAABBBCCCDDDEEE

Examples with solutions for Area of a Trapezoid: Calculate The Missing Side based on the formula

Exercise #1

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 #2

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

252−135=9AB 252-135=9AB

117=9AB 117=9AB

We divide the two sections by 9

13=AB 13=AB

Answer

13

Exercise #3

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 trapezoid will be equal to: S=(AB+DC)2×h S=\frac{(AB+DC)}{2}\times h

We insert the available data into the formula:

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

We then multiply by 2 in order to remove the fraction:

Lastly we again multiply by 2:

5.5=AB+4 5.5=AB+4

5.5−4=AB 5.5-4=AB

1.5=AB 1.5=AB

Answer

1.5 1.5 cm

Exercise #4

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 #5

The area of trapezoid ABCD is equal to 45 cm².

The base of the trapezoid BC is equal to 4 cm.

The base of the trapezoid AD is equal to 6 cm.

Calculate the length of AE.

S=45S=45S=45444666AAABBBCCCDDDEEE

Video Solution

Answer

9

Question 1

The area of trapezoid

ABCD is 100 cm².

The height of trapezoid CE is 8 cm.

The base of trapezoid AD is 15 cm.

Calculate the length of BC.

S=100S=100S=100151515888BBBCCCDDDAAAEEE

Question 2

Given that the area of the trapezoid ABCD is 67 cm².

The height of the trapezoid is 8 cm.

The length of one of the bases is 12cm

What is the length of the other base?

S=67S=67S=67121212888AAABBBCCCDDD

Question 3

The area of the trapezoid ABCD is 32 cm².

The height of ABCD is 4 cm.

The base of ABCD is 6 cm.

Calculate the length of the second base.

S=32S=32S=32666444BBBCCCDDDAAAEEE

Question 4

The area of the trapezoid in the drawing is equal to 18 cm².

Find AE

333666AAABBBCCCDDDEEE

Question 5

The area of the trapezoid in the figure is 27.5 cm².

Calculate the side marked in red.

555666

Exercise #6

The area of trapezoid

ABCD is 100 cm².

The height of trapezoid CE is 8 cm.

The base of trapezoid AD is 15 cm.

Calculate the length of BC.

S=100S=100S=100151515888BBBCCCDDDAAAEEE

Video Solution

Answer

10

Exercise #7

Given that the area of the trapezoid ABCD is 67 cm².

The height of the trapezoid is 8 cm.

The length of one of the bases is 12cm

What is the length of the other base?

S=67S=67S=67121212888AAABBBCCCDDD

Video Solution

Answer

4.75

Exercise #8

The area of the trapezoid ABCD is 32 cm².

The height of ABCD is 4 cm.

The base of ABCD is 6 cm.

Calculate the length of the second base.

S=32S=32S=32666444BBBCCCDDDAAAEEE

Video Solution

Answer

5.5X

Exercise #9

The area of the trapezoid in the drawing is equal to 18 cm².

Find AE

333666AAABBBCCCDDDEEE

Video Solution

Answer

4 4 cm

Exercise #10

The area of the trapezoid in the figure is 27.5 cm².

Calculate the side marked in red.

555666

Video Solution

Answer

5 5 cm

Question 1

The area of the trapezoid in the diagram is equal to 12 cm².

What is the length of the side marked in red?

555777

Question 2

The area of the trapezoid in the diagram is 42 cm².

Calculate BC.

555999AAABBBCCCDDD

Question 3

The area of the trapezoid in the drawing is equal to 300 cm².

Find the size of the other base of the trapezium.

151515151515

Question 4

The area of the trapezoid in the diagram is 63 cm².

Calculate the length of side BC.

888101010AAABBBCCCDDD

Question 5

Given the trapeze in front of you:

AAABBBCCCDDD12777

Given h=7, CD=12.

Since the area of the trapezoid ABCD is equal to 77.

Find the length of the side AB.

Exercise #11

The area of the trapezoid in the diagram is equal to 12 cm².

What is the length of the side marked in red?

555777

Video Solution

Answer

2 2 cm

Exercise #12

The area of the trapezoid in the diagram is 42 cm².

Calculate BC.

555999AAABBBCCCDDD

Video Solution

Answer

6 6 cm

Exercise #13

The area of the trapezoid in the drawing is equal to 300 cm².

Find the size of the other base of the trapezium.

151515151515

Video Solution

Answer

25 25 cm

Exercise #14

The area of the trapezoid in the diagram is 63 cm².

Calculate the length of side BC.

888101010AAABBBCCCDDD

Video Solution

Answer

7 7 cm

Exercise #15

Given the trapeze in front of you:

AAABBBCCCDDD12777

Given h=7, CD=12.

Since the area of the trapezoid ABCD is equal to 77.

Find the length of the side AB.

Video Solution

Answer

10

Question 1

Given the trapeze in front of you:

AAABBBCCCDDD9808

Given h=8, AB=9.

Since the area of the trapezoid ABCD is equal to 80.

Find the length of the side DC.

Question 2

Given the trapeze in front of you:

AAABBBCCCDDD1112010

Given h=10, AB=11.

Since the area of the trapezoid ABCD is equal to 120.

Find the length of the side DC.

Question 3

Given the trapeze in front of you:

AAABBBCCCDDD8808

Given h=8, AB=8.

Since the area of the trapezoid ABCD is equal to 80.

Find the length of the side DC.

Question 4

Calculate X according to the data in the figure:

S=60S=60S=60888141414555XXX

Question 5

Calculate X according to the data in the diagram:

XXX777555

Exercise #16

Given the trapeze in front of you:

AAABBBCCCDDD9808

Given h=8, AB=9.

Since the area of the trapezoid ABCD is equal to 80.

Find the length of the side DC.

Video Solution

Answer

10

Exercise #17

Given the trapeze in front of you:

AAABBBCCCDDD1112010

Given h=10, AB=11.

Since the area of the trapezoid ABCD is equal to 120.

Find the length of the side DC.

Video Solution

Answer

13

Exercise #18

Given the trapeze in front of you:

AAABBBCCCDDD8808

Given h=8, AB=8.

Since the area of the trapezoid ABCD is equal to 80.

Find the length of the side DC.

Video Solution

Answer

7

Exercise #19

Calculate X according to the data in the figure:

S=60S=60S=60888141414555XXX

Video Solution

Answer

2

Exercise #20

Calculate X according to the data in the diagram:

XXX777555

Video Solution

Answer

6 6