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.
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.
Complete the sentence:
To find the area of a right triangle, one must multiply ________________ by each other and divide by 2.
In 7th grade we focus on learning about several polygons (click on the links for in-depth reading):
The formula for calculating the area of a polygon varies according to the polygon in question. (Click on the titles to read the full articles including examples and practice)
A parallelogram has a length equal to 6 cm and a height equal to 4.5 cm.
Calculate the area of the parallelogram.
Calculate the area of the parallelogram using the data in the figure:
Find the area of the parallelogram based on the data in the figure:
The formula for calculating the area of a rectangle is: width X length.
The formula for calculating the area of any triangle: base X height divided by 2
Calculate the area of the parallelogram using the data in the figure:
Calculate the area of the parallelogram using the data in the figure:
Calculate the area of the parallelogram using the data in the figure:
In the case of a right triangle's area, it's the same formula, but the height is actually one of the sides
The area of a parallelogram is calculated by multiplying one of its sides by the height.
For example in the drawing, you can calculate the area of the parallelogram by multiplying DC by h1 and then dividing by 2, or by multiplying BC by h2 and then dividing by 2
Calculate the area of the parallelogram using the data in the figure:
Calculate the area of the right triangle below:
Calculate the area of the trapezoid.
The formula for calculating the area of a trapezoid is the sum of the two bases X the height divided by 2
Calculate the area of the parallelogram according to the data in the diagram.
Calculate the area of the trapezoid.
Calculate the area of the parallelogram based on the data in the figure:
Calculate the area of the right triangle below:
Due to the fact that AB is perpendicular to BC and forms a 90-degree angle,
it can be argued that AB is the height of the triangle.
Hence we can calculate the area as follows:
24 cm²
Calculate the area of the triangle ABC using the data in the figure.
First, let's remember the formula for the area of a triangle:
(the side * the height that descends to the side) /2
In the question, we have three pieces of data, but one of them is redundant!
We only have one height, the line that forms a 90-degree angle - AD,
The side to which the height descends is CB,
Therefore, we can use them in our calculation:
36 cm²
The trapezoid ABCD is shown below.
AB = 2.5 cm
DC = 4 cm
Height (h) = 6 cm
Calculate the area of the trapezoid.
First, let's remind ourselves of the formula for the area of a trapezoid:
We substitute the given values into the formula:
(2.5+4)*6 =
6.5*6=
39/2 =
19.5
The trapezoid ABCD is shown below.
Base AB = 6 cm
Base DC = 10 cm
Height (h) = 5 cm
Calculate the area of the trapezoid.
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
40 cm²
What is the area of the triangle in the drawing?
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
17.5