Areas of Polygons for 7th Grade

Areas of Polygons

Polygon Definition

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:

We can divide the area of the required polygon into several areas of polygons that we are familiar with, calculate the areas separately, and then add them together to obtain the final area.
We can try to "complete" the area of the required polygon into another polygon whose area we know how to calculate, and the proceed to subtract the area we added. This way, we can obtain the area of the original polygon.

Example

Let's demonstrate this using a simple exercise:

Diagram of a composite shape divided into two rectangles, with dimensions labeled. The left rectangle has dimensions 7 by 4 with an area (A) of 28, and the right rectangle has dimensions 3 by 6 with an area (A) of 18. The diagram illustrates how to calculate areas of composite polygons by dividing them into simpler shapes. Featured in a tutorial on calculating areas of polygons.

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.

Detailed explanation

Start practice

Test yourself on area of a rectangle!

Calculate the area of the trapezoid.

Practice more now

In 7th grade we focus on learning about several polygons (click on the links for in-depth reading):

How to calculate areas of polygons

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)

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Test your knowledge

Question 1

Calculate the area of the trapezoid.

Question 2

Complete the sentence:

To find the area of a right triangle, one must multiply ________________ by each other and divide by 2.

Question 3

Given the following rectangle:

Find the area of the rectangle.

Calculating Rectangle Area

The formula for calculating the area of a rectangle is: width X length.

$S=w\cdot h$

Calculating the area of any triangle

The formula for calculating the area of any triangle: base X height divided by 2

$S={{Base \cdot h}\over 2}$

Do you know what the answer is?

Question 1

Given the following rectangle:

Find the area of the rectangle.

Question 2

Given the following rectangle:

Find the area of the rectangle.

Question 3

Given the following rectangle:

Find the area of the rectangle.

Calculating the area of a right triangle

In the case of a right triangle's area, it's the same formula, but the height is actually one of the sides

Calculating the Area of a Parallelogram

The area of a parallelogram is calculated by multiplying one of its sides by the height.

$S={{Base \cdot h}\over 2}$

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

Check your understanding

Question 1

Calculate the area of the right triangle below:

Question 2

Calculate the area of the parallelogram according to the data in the diagram.

Question 3

Calculate the area of the parallelogram using the data in the figure:

Calculating the Area of a Trapezoid

The formula for calculating the area of a trapezoid is the sum of the two bases X the height divided by 2

$S={{(Base{_1} + Base{_2}) \cdot h}\over 2}$

A1 - How do you calculate the area of a new trapezoid

Do you think you will be able to solve it?

Question 1

Find the area of the parallelogram based on the data in the figure:

Question 2

Calculate the area of the parallelogram using the data in the figure:

Question 3

Look at the rectangle ABCD below.

Side AB is 6 cm long and side BC is 4 cm long.

What is the area of the rectangle?

Examples with solutions for Areas of Polygons for 7th Grade

Exercise #1

Calculate the area of the trapezoid.

Video Solution

Step-by-Step Solution

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.

Answer

Cannot be calculated.

Exercise #2

Calculate the area of the trapezoid.

Video Solution

Step-by-Step Solution

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.

Answer

It cannot be calculated.

Exercise #3

Complete the sentence:

To find the area of a right triangle, one must multiply ________________ by each other and divide by 2.

Step-by-Step Solution

To solve this problem, begin by identifying the elements involved in calculating the area of a right triangle. In a right triangle, the two sides that form the right angle are known as the legs. These legs act as the base and height of the triangle.

The formula for the area of a triangle is given by:

A = \frac{1}{2} \times \text{base} \times \text{height}

In the case of a right triangle, the base and height are the two legs. Therefore, the process of finding the area involves multiplying the lengths of the two legs together and then dividing the product by 2.

Based on this analysis, the correct way to complete the sentence in the problem is:

To find the area of a right triangle, one must multiply the two legs by each other and divide by 2.

Answer

the two legs

Exercise #4

Given the following rectangle:

Find the area of the rectangle.

Video Solution

Step-by-Step Solution

We will use the formula to calculate the area of a rectangle: length times width

$9\times6=54$

Answer

Exercise #5

Given the following rectangle:

Find the area of the rectangle.

Video Solution

Step-by-Step Solution

Let's calculate the area of the rectangle by multiplying the length by the width:

$4\times8=32$

Answer

Start practice

Areas of Polygons for 7th Grade