Area of a Trapezoid: Applying 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 shapesCalculate The Missing Side based on the formula
Question 1

The trapezoid ABCD is shown below.

Base AB = 6 cm

Base DC = 10 cm

Height (h) = 5 cm

Calculate the area of the trapezoid.

666101010h=5h=5h=5AAABBBCCCDDD

Question 2

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

Question 3

What is the area of the trapezoid in the figure?

777151515222AAABBBCCCDDDEEE

Question 4

Given the trapezoid:

999121212555AAABBBCCCDDDEEE

What is the area?

Question 5

What is the area of the trapezoid in the figure?

222999777AAABBBCCCDDD

Examples with solutions for Area of a Trapezoid: Applying the formula

Exercise #1

The trapezoid ABCD is shown below.

Base AB = 6 cm

Base DC = 10 cm

Height (h) = 5 cm

Calculate the area of the trapezoid.

666101010h=5h=5h=5AAABBBCCCDDD

Video Solution

Step-by-Step Solution

First, we need to remind ourselves of how to work out the area of a trapezoid:

Formula for calculating trapezoid area

Now let's substitute the given data into the formula:

(10+6)*5 =
2

Let's start with the upper part of the equation:

16*5 = 80

80/2 = 40

Answer

40 cm²

Exercise #2

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 #3

What is the area of the trapezoid in the figure?

777151515222AAABBBCCCDDDEEE

Video Solution

Step-by-Step Solution

We use the following 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 #4

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 #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 insert the existing data into 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.

Question 1

Given the following trapezoid:

AAABBBCCCDDD57

Find the area of the trapezoid ABCD.

Question 2

The trapezoid ABCD is shown below.

AB = 5 cm

DC = 9 cm

Height (h) = 7 cm

Calculate the area of the trapezoid.

555999h=7h=7h=7AAABBBCCCDDD

Question 3

What is the area of the trapezoid in the diagram below?

777333AAABBBCCCDDDEEEFFF4

Question 4

What is the area of the trapezoid in the diagram?

555138

Question 5

What is the area of the trapezoid in the figure?

666777121212555444

Exercise #6

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

Exercise #7

The trapezoid ABCD is shown below.

AB = 5 cm

DC = 9 cm

Height (h) = 7 cm

Calculate the area of the trapezoid.

555999h=7h=7h=7AAABBBCCCDDD

Video Solution

Answer

49 cm

Exercise #8

What is the area of the trapezoid in the diagram below?

777333AAABBBCCCDDDEEEFFF4

Video Solution

Answer

16.5 16.5 cm²

Exercise #9

What is the area of the trapezoid in the diagram?

555138

Video Solution

Answer

52.5 52.5 cm²

Exercise #10

What is the area of the trapezoid in the figure?

666777121212555444

Video Solution

Answer

36 36 cm².

Question 1

What is the area of the trapezoid in the figure?

6.56.56.5101010444AAABBBCCCDDDEEE

Question 2

What is the area of the trapezoid ABCD?

999121212555AAABBBCCCDDDEEE

Question 3

The trapezoid ABCD is shown below.

The height of ABCD is 6 cm.

The base BC is equal to 4 cm.

The base AD is equal to 8 cm.

Calculate the area of trapezoid ABCD.

444888666BBBCCCDDDAAAEEE

Question 4

Calculate the area of the trapezoid.

555888333

Question 5

Given the following trapezoid:

AAABBBCCCDDD584

Calculate the area of the trapezoid ABCD.

Exercise #11

What is the area of the trapezoid in the figure?

6.56.56.5101010444AAABBBCCCDDDEEE

Video Solution

Answer

33 33 cm².

Exercise #12

What is the area of the trapezoid ABCD?

999121212555AAABBBCCCDDDEEE

Video Solution

Answer

52.5

Exercise #13

The trapezoid ABCD is shown below.

The height of ABCD is 6 cm.

The base BC is equal to 4 cm.

The base AD is equal to 8 cm.

Calculate the area of trapezoid ABCD.

444888666BBBCCCDDDAAAEEE

Video Solution

Answer

36

Exercise #14

Calculate the area of the trapezoid.

555888333

Video Solution

Answer

19 1/2

Exercise #15

Given the following trapezoid:

AAABBBCCCDDD584

Calculate the area of the trapezoid ABCD.

Video Solution

Answer

26

Question 1

Given the following trapezoid:

AAABBBCCCDDD795

Calculate the area of the trapezoid ABCD.

Question 2

Given the following trapezoid:

AAABBBCCCDDD683

Calculate the area of the trapezoid ABCD.

Question 3

Given the following trapezoid:

AAABBBCCCDDD5104

Calculate the area of the trapezoid ABCD.

Question 4

Given the following trapezoid:

AAABBBCCCDDD7115

Calculate the area of the trapezoid ABCD.

Question 5

What is the area of the trapezoid ABCD?

111111AAABBBCCCDDDEEE2518

Exercise #16

Given the following trapezoid:

AAABBBCCCDDD795

Calculate the area of the trapezoid ABCD.

Video Solution

Answer

40

Exercise #17

Given the following trapezoid:

AAABBBCCCDDD683

Calculate the area of the trapezoid ABCD.

Video Solution

Answer

21

Exercise #18

Given the following trapezoid:

AAABBBCCCDDD5104

Calculate the area of the trapezoid ABCD.

Video Solution

Answer

30

Exercise #19

Given the following trapezoid:

AAABBBCCCDDD7115

Calculate the area of the trapezoid ABCD.

Video Solution

Answer

45

Exercise #20

What is the area of the trapezoid ABCD?

111111AAABBBCCCDDDEEE2518

Video Solution

Answer

236.5 236.5 cm².