Areas of Polygons for 7th Grade - Examples, Exercises and Solutions

Understanding Areas of Polygons for 7th Grade

Complete explanation with examples

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

Practice Areas of Polygons for 7th Grade

Test your knowledge with 94 quizzes

Calculate the area of the triangle ABC using the data in the figure.

121212888999AAABBBCCCDDD

Examples with solutions for Areas of Polygons for 7th Grade

Step-by-step solutions included
Exercise #1

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?
666444AAABBBCCCDDD

Step-by-Step Solution

Remember that the formula for the area of a rectangle is width times height

 

We are given that the width of the rectangle is 6

and that the length of the rectangle is 4

 Therefore we calculate:

6*4=24

Answer:

24 cm²

Video Solution
Exercise #2

Look at the rectangle ABCD below.

Side AB is 4.5 cm long and side BC is 2 cm long.

What is the area of the rectangle?
4.54.54.5222AAABBBCCCDDD

Step-by-Step Solution

We begin by multiplying side AB by side BC

We then substitute the given data and we obtain the following:

4.5×2=9 4.5\times2=9

Hence the area of rectangle ABCD equals 9

Answer:

9 cm²

Video Solution
Exercise #3

Look at rectangle ABCD below.

Side AB is 10 cm long and side BC is 2.5 cm long.

What is the area of the rectangle?
1010102.52.52.5AAABBBCCCDDD

Step-by-Step Solution

Let's begin by multiplying side AB by side BC

If we insert the known data into the above equation we should obtain the following:

10×2.5=25 10\times2.5=25

Thus the area of rectangle ABCD equals 25.

Answer:

25 cm²

Video Solution
Exercise #4

The triangle ABC is given below.
AC = 10 cm

AD = 3 cm

BC = 11.6 cm
What is the area of the triangle?

11.611.611.6101010333AAABBBCCCDDD

Step-by-Step Solution

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:

CB×AD2 \frac{CB\times AD}{2}

11.6×32 \frac{11.6\times3}{2}

34.82=17.4 \frac{34.8}{2}=17.4

Answer:

17.4

Video Solution
Exercise #5

What is the area of the given triangle?

555999666

Step-by-Step Solution

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:

A1- How to find the area of a triangleThe 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:

6×52=302=15 \frac{6\times5}{2}=\frac{30}{2}=15

Answer:

15

Video Solution

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Applying the formula Calculate The Missing Side based on the formula Calculating in two ways Finding Area based off Perimeter and Vice Versa Using additional geometric shapes Using congruence and similarity Using external height Using Pythagoras' theorem Using ratios for calculation Using variables Verifying whether or not the formula is applicable Applying the formula A shape consisting of several shapes (requiring the same formula) Calculate The Missing Side based on the formula Calculation using the diagonal Extended distributive law Finding Area based off Perimeter and Vice Versa Subtraction or addition to a larger shape Using additional geometric shapes Using Pythagoras' theorem Using ratios for calculation Using short multiplication formulas Using variables Worded problems Applying the formula Calculate The Missing Side based on the formula Finding Area based off Perimeter and Vice Versa Subtraction or addition to a larger shape Suggesting options for terms when the formula result is known Using additional geometric shapes Using Pythagoras' theorem Using ratios for calculation Using variables Applying the formula Ascertaining whether or not there are errors in the data Calculate The Missing Side based on the formula Calculating in two ways Extended distributive law Finding Area based off Perimeter and Vice Versa How many times does the shape fit inside of another shape? Identifying and defining elements Subtraction or addition to a larger shape Using additional geometric shapes Using congruence and similarity Using Pythagoras' theorem Using ratios for calculation Using variables Worded problems