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.
What is the area of the given triangle?
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)
What is the area of the triangle in the drawing?
Calculate the area of the parallelogram based on the data in the figure:
A parallelogram has a length equal to 6 cm and a height equal to 4.5 cm.
Calculate the area of the parallelogram.
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
Find the area of the parallelogram based on 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 parallelogram using the data in the figure:
Calculate the area of the parallelogram using the data in the figure:
The formula for calculating the area of a trapezoid is the sum of the two bases X the height divided by 2
The triangle ABC is given below.
AC = 10 cm
AD = 3 cm
BC = 11.6 cm
What is the area of the triangle?
The width of a rectangle is equal to 15 cm and its length is 3 cm.
Calculate the area of the rectangle.
The width of a rectangle is equal to \( 18 \)cm and its length is \( 2~ \)cm.
Calculate the area of the rectangle.
What is the area of the given triangle?
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:
15
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
The triangle ABC is given below.
AC = 10 cm
AD = 3 cm
BC = 11.6 cm
What is the area of the triangle?
The triangle we are looking at is the large triangle - ABC
The triangle is formed by three sides AB, BC, and CA.
Now let's remember what we need for the calculation of a triangular area:
(side x the height that descends from the side)/2
Therefore, the first thing we must find is a suitable height and side.
We are given the side AC, but there is no descending height, so it is not useful to us.
The side AB is not given,
And so we are left with the side BC, which is given.
From the side BC descends the height AD (the two form a 90-degree angle).
It can be argued that BC is also a height, but if we delve deeper it seems that CD can be a height in the triangle ADC,
and BD is a height in the triangle ADB (both are the sides of a right triangle, therefore they are the height and the side).
As we do not know if the triangle is isosceles or not, it is also not possible to know if CD=DB, or what their ratio is, and this theory fails.
Let's remember again the formula for triangular area and replace the data we have in the formula:
(side* the height that descends from the side)/2
Now we replace the existing data in this formula:
17.4
The width of a rectangle is equal to 15 cm and its length is 3 cm.
Calculate the area of the rectangle.
To calculate the area of the rectangle, we multiply the length by the width:
45
Calculate the area of the trapezoid.
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.
Cannot be calculated.