Area of a Trapezoid: Calculate The Missing Side based on 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.

Question 2

Given the trapezoid in front of you:

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.

Question 4

Given the trapezoid:

What is the height?

Question 5

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

Find AE

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.

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:

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

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

We multiply the equation by 2:

$60=(4+8)h$

$60=12h$

We divide the two sections by 12:

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

$5=h$

Answer

Exercise #2

Given the trapezoid in front of you:

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

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

We input the data we are given:

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

We multiply the equation by 2:

$252=9AB+135$

$252-135=9AB$

$117=9AB$

We divide the two sections by 9

$13=AB$

Answer

Exercise #3

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

Work out the length of the side marked in red.

Video Solution

Step-by-Step Solution

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

We insert the available data into the formula:

$1.375=\frac{AB+4}{2}\times0.5$

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

Lastly we again multiply by 2:

$5.5=AB+4$

$5.5-4=AB$

$1.5=AB$

Answer

$1.5$ cm

Exercise #4

Given the trapezoid:

What is the height?

Video Solution

Step-by-Step Solution

Formula for the area of a trapezoid:

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

We substitute the data into the formula

$\frac{9+6}{2}\times h=30$

We solve:

$\frac{15}{2}\times h=30$

$7\frac{1}{2}\times h=30$

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

$h=4$

Answer

Exercise #5

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

Find AE

Video Solution

Answer

$4$ cm

Question 1

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

Calculate the side marked in red.

Question 2

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

What is the length of the side marked in red?

Question 3

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

Calculate BC.

Question 4

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

Find the size of the other base of the trapezium.

Question 5

Answer

$7$ cm

Question 1

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.

Question 2

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.

Question 3

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?

Question 4

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.

Question 5

Given the trapeze in front of you:

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 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.

Video Solution

Answer

Exercise #12

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.

Video Solution

Answer

Exercise #13

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?

Video Solution

Answer

4.75

Exercise #14

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.

Video Solution

Answer

5.5

Exercise #15

Given the trapeze in front of you:

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

Question 1

Given the trapeze in front of you:

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:

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:

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

The area of the trapezoid in the diagram is 70 cm².

Calculate the length of AB.

Question 5

The area of the trapezoid in the figure is equal to 52.5 cm².

Answer

Exercise #19

The area of the trapezoid in the diagram is 70 cm².

Calculate the length of AB.

Video Solution

Answer

$9$ cm

Exercise #20

The area of the trapezoid in the figure is equal to 52.5 cm².

Calculate DE.

Video Solution

Answer

$6$ cm