How do we calculate the area of complex shapes?

This question is a bit confusing. We need start by identifying which parts of the data are relevant to us.

Remember the formula for the area of a triangle:

The height is a straight line that comes out of an angle and forms a right angle with the opposite side.

In the drawing we have a height of 6.

It goes down to the opposite side whose length is 5.

And therefore, these are the data points that we will use.

We replace in the formula:

$\frac{6\times5}{2}=\frac{30}{2}=15$

First, we will identify the data points we need to be able to find the area of the triangle.

the formula for the area of the triangle: height*opposite side / 2

Since it is a right triangle, we know that the straight sides are actually also the heights between each other, that is, the side that measures 5 and the side that measures 7.

We multiply the legs and divide by 2

$\frac{5\times7}{2}=\frac{35}{2}=17.5$

In this particular problem, despite being given certain measurements, the diagram lacks sufficient clarity to identify which corresponds definitively as the base and which as the perpendicular height of the parallelogram. This insufficiency means that without further context or labeling to avoid assumptions that may lead to error, it is not feasible to calculate the area confidently using the standard formula.

Thus, the answer to the problem is that it is not possible to calculate the area with the provided data.

To solve this problem, let's apply the formula for the area of a parallelogram:

The formula for the area of a parallelogram is $\text{Area} = \text{base} \times \text{height}$.

Here, the base of the parallelogram is 6 cm, and the height is 4.5 cm.

Substituting these values into the formula gives:

$\text{Area} = 6 \times 4.5$

Performing the multiplication:

$\text{Area} = 27$ square centimeters.

Therefore, the area of the parallelogram is $27 \, \text{cm}^2$.

Referring to the given multiple-choice answers, the correct choice is:

Choice 3: $27$.

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 provides us with a base ($b$) of 7 units and a height ($h$) of 5 units, perpendicular to this base.
Step 2: We'll apply the formula for the area of a parallelogram, which is $\text{Area} = b \times h$.
Step 3: Substituting the given values, $\text{Area} = 7 \times 5 = 35$.

Therefore, the area of the parallelogram is $35$ square units.