Area of a Trapezoid - Examples, Exercises and Solutions

Formula for the area of a trapezoid:

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

We substitute the data into the formula and solve:

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

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 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.

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 $26$.

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

• Step 1: Identify the lengths of the trapezoid's bases: $AB = 7$ and $CD = 9$.
• Step 2: Identify the height of the trapezoid: $AD = 5$.
• Step 3: Apply the trapezoid area formula: $A = \frac{1}{2} \times (b_1 + b_2) \times h$.
• Step 4: Calculate the area using the values from Steps 1 and 2.

Now, let us work through each step:
Step 1: The length of base $AB$ is $(b_1 = 7)$ units, and the length of base $CD$ is $(b_2 = 9)$ units.
Step 2: The height $AD$ is $(h = 5)$ units.

Step 3: Substitute the known values into the formula for the area of a trapezoid:
$A = \frac{1}{2} \times (7 + 9) \times 5$

Step 4: Calculate the results:
$A = \frac{1}{2} \times 16 \times 5 = \frac{1}{2} \times 80 = 40$

Therefore, the area of trapezoid ABCD is $\mathbf{40}$ square units.

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

• Step 1: Recall the formula for the area of a trapezoid.
• Step 2: Substitute the given values into the formula.
• Step 3: Calculate the area using arithmetic operations.

Let's work through each step:
Step 1: The formula for the area of a trapezoid is given by:
$\text{Area} = \frac{1}{2} \times (\text{Base}_1 + \text{Base}_2) \times \text{Height}$
Step 2: Plug in the values: $\text{Base}_1 = AB = 6$, $\text{Base}_2 = CD = 8$, and the height $AD = 3$.
$\text{Area} = \frac{1}{2} \times (6 + 8) \times 3$
Step 3: Perform the calculations:
$\text{Area} = \frac{1}{2} \times 14 \times 3 = \frac{1}{2} \times 42 = 21$

Therefore, the area of trapezoid $ABCD$ is $21$.

To solve this problem, we'll calculate the area of trapezoid ABCD using the appropriate formula.

The formula for the area $A$ of a trapezoid is given by:

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

Substituting the given values into the formula, we have:

$A = \frac{1}{2} \times (5 + 10) \times 4$

First, calculate the sum of the bases:

$5 + 10 = 15$

Multiply by the height, and then take half:

$A = \frac{1}{2} \times 15 \times 4 = \frac{1}{2} \times 60 = 30$

Therefore, the area of the trapezoid ABCD is 30 square units.

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

Given:

• Base $AB = 7$
• Base $CD = 11$
• Height $= 5$

Apply the trapezoid area formula:

The formula for the area of a trapezoid is:

Substitute the values into the formula:

Simplify the expression:

Calculate:

Finally, compute the area:

Thus, the area of trapezoid ABCD is $45$.

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 $52.5$ .