Right-Angled Trapezoid Area Practice Problems & 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 $36 \, \text{cm}^2$.