Area of a Trapezoid - Examples, Exercises and Solutions

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.

To find the area of the trapezoid, we would ideally use the formula:

$A = \frac{1}{2} \times (b_1 + b_2) \times h$

where $b_1$ and $b_2$ are the lengths of the two parallel sides and $h$ is the height. However, the given information is incomplete for these purposes.

The numbers provided ($6$, $7$, $12$, and $5$) do not clearly designate which are the bases and what is the height. Without this information, the dimensions cannot be definitively identified, making it impossible to calculate the area accurately.

Thus, the problem, based on the given diagram and information, cannot be solved for the area of the trapezoid.

Therefore, the correct answer is: It cannot be calculated.

To solve this problem, we'll calculate the area of the trapezoid using the standard formula:

• Step 1: Identify the given dimensions:
• Shorter base $b_1 = 5$.
• Longer base $b_2 = 8$.
• Height $h = 3$.

Step 2: We apply the trapezoid area formula, which is:

$A = \frac{1}{2} \times (b_1 + b_2) \times h$.

Step 3: Substitute the given values into the formula:

$A = \frac{1}{2} \times (5 + 8) \times 3$.

Step 4: Perform the calculations:

$A = \frac{1}{2} \times 13 \times 3$.

$A = \frac{1}{2} \times 39$.

$A = 19.5$ or $19 \frac{1}{2}$.

The area of the trapezoid is $19 \frac{1}{2}$.

To solve this problem, we'll follow these steps:

• Identify the given measurements: the lengths of the parallel sides (bases) and the height.
• Use the trapezoid area formula to calculate the area.
• Perform the necessary arithmetic to find the numerical answer.

Now, let's work through each step:
Step 1: The given measurements are $\text{Base}_1 = 9$, $\text{Base}_2 = 12$, and the height = 5.
Step 2: The formula for the area of a trapezoid is $\text{Area} = \frac{1}{2} \times (\text{Base}_1 + \text{Base}_2) \times \text{Height}$.
Step 3: Substituting the numbers into the formula, we have:
$\text{Area} = \frac{1}{2} \times (9 + 12) \times 5$

Calculating inside the parentheses first:
$9 + 12 = 21$

Then multiply by the height:
$21 \times 5 = 105$

Finally, multiply by one-half:
$\frac{1}{2} \times 105 = 52.5$

Therefore, the area of trapezoid $ABCD$ is $52.5$ .

To solve this problem, we'll follow these steps:

• Step 1: Identify the given information
• Step 2: Apply the appropriate formula
• Step 3: Perform the necessary calculations

Now, let's work through each step:

Step 1: The problem gives us the height of the trapezoid as $6 \, \text{cm}$, base BC as $4 \, \text{cm}$ and base AD as $8 \, \text{cm}$.

Step 2: We'll use the formula for the area of a trapezoid:

$A = \frac{1}{2} \times (\text{base}_1 + \text{base}_2) \times \text{height}$

Step 3: Substituting the given values into the formula:

$A = \frac{1}{2} \times (4 + 8) \times 6$

Calculating further,

$A = \frac{1}{2} \times 12 \times 6$

$A = \frac{1}{2} \times 72$

$A = 36 \, \text{cm}^2$

Therefore, the area of the trapezoid ABCD is $36 \, \text{cm}^2$.

Formula for the area of a trapezoid:

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

We substitute the data into the formula and solve:

$\frac{9+12}{2}\times5=\frac{21}{2}\times5=\frac{105}{2}=52.5$

To determine the area of the trapezoid, we will follow these steps:

• Step 1: Identify the provided dimensions of the trapezoid.
• Step 2: Apply the formula for the area of a trapezoid.
• Step 3: Perform the arithmetic to calculate the area.

Let's proceed through these steps:

Step 1: Identify the dimensions
The given dimensions from the diagram are:
Height $h = 3$ cm.
One base $b_1 = 4$ cm.
The other base $b_2 = 7$ cm.

Step 2: Apply the area formula
To find the area $A$ of the trapezoid, use the formula:
$A = \frac{1}{2} \times (b_1 + b_2) \times h$

Step 3: Calculation
Substituting the known values into the formula:
$A = \frac{1}{2} \times (4 + 7) \times 3$

Simplify the expression:
$A = \frac{1}{2} \times 11 \times 3$

Calculate the result:
$A = \frac{1}{2} \times 33 = \frac{33}{2} = 16.5$ cm²

The area of the trapezoid is therefore $16.5$ cm².

Given the choices, this corresponds to choice : $16.5$ cm².

Therefore, the correct solution to the problem is $16.5$ cm².

To find the area of the trapezoid, we will follow these steps:

• Step 1: Identify the given dimensions of the trapezoid.
• Step 2: Apply the area formula for a trapezoid using these dimensions.
• Step 3: Perform the calculation to determine the area.

Let's work through each step more clearly:
Step 1: From the problem, we identify that the trapezoid has one base $b_1 = 13$ units, another base $b_2 = 8$ units, and its height $h = 5$ units.
Step 2: The formula for the area of a trapezoid is:

$A = \frac{1}{2} \times (b_1 + b_2) \times h$

Step 3: Substitute the values into the formula:

$A = \frac{1}{2} \times (13 + 8) \times 5$

$A = \frac{1}{2} \times 21 \times 5$

$A = \frac{1}{2} \times 105$

$A = 52.5 \, \text{units}^2$

Therefore, the area of the trapezoid is $52.5 \, \text{units}^2$.

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

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

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

To solve this problem, we'll follow these steps:

• Step 1: Identify the given information relevant to the trapezoid.
• Step 2: Apply the appropriate formula for the area of a trapezoid.
• Step 3: Perform the necessary calculations to find the area.

Now, let's work through each step:
Step 1: The problem gives us two bases, $b_1 = 6$ cm and $b_2 = 12$ cm, and a height $h = 4$ cm.
Step 2: We'll use the formula for the area of a trapezoid: $A = \frac{1}{2} \cdot (b_1 + b_2) \cdot h$
Step 3: Substituting in the given values: $A = \frac{1}{2} \cdot (6 + 12) \cdot 4 = \frac{1}{2} \cdot 18 \cdot 4 = \frac{72}{2} = 36 \text{ cm}^2$

Therefore, the solution to the problem is $36$ cm².

To solve this problem, we'll compute the area of the trapezoid using the given dimensions and the area formula:

• Step 1: Identify the given dimensions:
• Base $b_1 = 10$ cm
• Base $b_2 = 6.5$ cm
• Height $h = 4$ cm
• Step 2: Use the trapezoid area formula:

The formula for the area of a trapezoid is $A = \frac{1}{2}(b_1 + b_2)h$.

• Step 3: Substitute the given values into the formula:

$A = \frac{1}{2}(10 + 6.5) \times 4$

• Step 4: Calculate the area:

First, calculate the sum of the bases: $10 + 6.5 = 16.5$.

Next, multiply by the height: $16.5 \times 4 = 66$.

Finally, divide by 2 to get the area: $\frac{66}{2} = 33$ cm².

Therefore, the area of the trapezoid is $33$ cm².

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



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

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

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

We substitute the given values into the formula:

(2.5+4)*6 =
6.5*6=
39/2 = 
19.5

The formula for the area of a trapezoid is:

We are given the following dimensions:

• Base $AB = 5$ cm
• Base $DC = 9$ cm
• Height $h = 7$ cm

Substituting these values into the formula, we have:

First, add the lengths of the bases:

Now substitute back into the formula:

Calculate the multiplication:

Then multiply by the height:

Thus, the area of the trapezoid is 49 cm$^2$.

To solve this problem, we follow these steps:

• Step 1: Identify the given dimensions of the trapezoid.
• Step 2: Use the formula for the area of a trapezoid.
• Step 3: Substitute the given values into the formula and calculate the area.

Now, let's work through these steps:

Step 1: We know from the problem that trapezoid ABCD has bases $AB = 5$ and $CD = 8$, with a height of $AD = 4$.

Step 2: The formula for the area of a trapezoid is:
$A = \frac{1}{2} \times (b_1 + b_2) \times h$

Step 3: Plugging in the values:
$A = \frac{1}{2} \times (5 + 8) \times 4 = \frac{1}{2} \times 13 \times 4 = \frac{52}{2} = 26$

Therefore, the area of the trapezoid ABCD is $26$.