A polygon defines a geometric shape that is made up of sides. In other words, under the umbrella of polygons fall the following square, rectangle, parallelogram, trapezoid, and many more.
Master rectangle area calculations and polygon area problems with step-by-step practice. Learn formulas, solve complex shapes, and build confidence in geometry.
A polygon defines a geometric shape that is made up of sides. In other words, under the umbrella of polygons fall the following square, rectangle, parallelogram, trapezoid, and many more.
For example, a triangle has 3 sides, every quadrilateral has 4 sides, and so on.
We have already learned to calculate the areas of standard polygons. There are also non-standard polygons, for which there is no specific formula. However, their area of complex shapes can be calculated using two methods:
Let's demonstrate this using a simple exercise:
Here is a drawing of a polygon.
We need to calculate its area. From the start, we can see that this is not a standard polygon, so we will use the first method to calculate its area. We will divide the polygon as shown in the drawing, and we should obtain two rectangles.
According to the data shown in the drawing, in the rectangle on the right side we obtain the side lengths of 3 and 6, therefore the area of the rectangle will be 18 (multiplication of the two values). In the rectangle on the left side we obtain the side lengths of 4 and 7, therefore the area of the rectangle will be 28 (multiplication of the two values). Thus, the total area of the polygon will be the sum of the two areas we calculated separately, meaning, 18+28=46.
AB = 6 cm
The height of the rectangle is 2 cm.
Calculate the area of the parallelogram.
AB = 10 cm
The height of the rectangle is 5 cm.
Calculate the area of the parallelogram.
To solve this problem, we'll apply the formula for the area of a parallelogram:
Let's proceed with the solution:
Step 1: The given base is 10 cm, and the height is 5 cm.
Step 2: The formula for the area of a parallelogram is .
Step 3: Substituting the provided values, we get:
Therefore, the area of the parallelogram is .
Answer:
50
Calculate the area of the following parallelogram:
To calculate the area of the parallelogram, we will simply apply the formula for the area of a parallelogram:
Apply the formula: .
Substitute the known values: .
Calculate the result: .
Therefore, the area of the parallelogram is .
Answer:
60 cm²
AB = 12 cm
The height of the rectangle is 4 cm.
Calculate the area of the parallelogram.
To solve this problem, we'll proceed as follows:
Let's perform each step:
Step 1: From the problem, we know:
Step 2: Use the formula for the area of a parallelogram:
Step 3: Plugging in the values of the base and height:
Therefore, the area of the parallelogram is .
Since this is a multiple-choice problem, the correct answer is Choice 2.
Answer:
48
AB = 15 cm
The height of the rectangle is 6 cm.
Calculate the area of the parallelogram.
To solve this problem, we'll follow these steps:
Now, let's work through each step:
Step 1: The base is equal to the length , which is . The height corresponding to this base is .
Step 2: We'll use the formula for the area of a parallelogram:
.
Step 3: Plugging in our values, we have:
.
Therefore, the solution to the problem is , which matches choice
Answer:
90
AB = 17 cm
The height of the rectangle is 8 cm.
Calculate the area of the parallelogram.
To solve this problem, we will calculate the area of the parallelogram using the given base and height dimensions.
Calculating the product, we have:
.
Therefore, the area of the parallelogram is .
Answer:
136