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

Question Types:
Area of a Parallelogram: Applying the formulaArea of a Parallelogram: Calculate The Missing Side based on the formulaArea of a Parallelogram: Calculating in two waysArea of a Parallelogram: Finding Area based off Perimeter and Vice VersaArea of a Parallelogram: Using additional geometric shapesArea of a Parallelogram: Using congruence and similarityArea of a Parallelogram: Using external heightArea of a Parallelogram: Using Pythagoras' theoremArea of a Parallelogram: Using ratios for calculationArea of a Parallelogram: Using variablesArea of a Parallelogram: Verifying whether or not the formula is applicableArea of a Rectangle: Applying the formulaArea of a Rectangle: A shape consisting of several shapes (requiring the same formula)Area of a Rectangle: Calculate The Missing Side based on the formulaArea of a Rectangle: Calculation using the diagonalArea of a Rectangle: Extended distributive lawArea of a Rectangle: Finding Area based off Perimeter and Vice VersaArea of a Rectangle: Subtraction or addition to a larger shapeArea of a Rectangle: Using additional geometric shapesArea of a Rectangle: Using Pythagoras' theoremArea of a Rectangle: Using ratios for calculationArea of a Rectangle: Using short multiplication formulasArea of a Rectangle: Using variablesArea of a Rectangle: Worded problemsArea of a Trapezoid: Applying the formulaArea of a Trapezoid: Calculate The Missing Side based on the formulaArea of a Trapezoid: Finding Area based off Perimeter and Vice VersaArea of a Trapezoid: Subtraction or addition to a larger shapeArea of a Trapezoid: Suggesting options for terms when the formula result is knownArea of a Trapezoid: Using additional geometric shapesArea of a Trapezoid: Using Pythagoras' theoremArea of a Trapezoid: Using ratios for calculationArea of a Trapezoid: Using variablesArea of a Triangle: Applying the formulaArea of a Triangle: Ascertaining whether or not there are errors in the dataArea of a Triangle: Calculate The Missing Side based on the formulaArea of a Triangle: Calculating in two waysArea of a Triangle: Finding Area based off Perimeter and Vice VersaArea of a Triangle: How many times does the shape fit inside of another shape?Area of a Triangle: Subtraction or addition to a larger shapeArea of a Triangle: Using additional geometric shapesArea of a Triangle: Using congruence and similarityArea of a Triangle: Using Pythagoras' theoremArea of a Triangle: Using ratios for calculationArea of a Triangle: Using variablesArea of a Triangle: Worded problems

Areas of Polygons

Polygon Definition

In fact, a polygon is any geometric shape made up of sides. In other words, under the umbrella of polygons fall the square, rectangle, parallelogram, trapezoid, and 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 get 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 subtract the area we added. This way, we can get 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 will get two rectangles.

According to the data shown in the drawing, in the rectangle on the right side we get 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 get 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.

Practice Areas of Polygons for 7th Grade

Examples with solutions for Areas of Polygons for 7th Grade

Exercise #1

Calculate the area of the right triangle below:

101010666888AAACCCBBB

Video Solution

Step-by-Step Solution

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:

AB×BC2=8×62=482=24 \frac{AB\times BC}{2}=\frac{8\times6}{2}=\frac{48}{2}=24

Answer

24 cm²

Exercise #2

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

121212888999AAABBBCCCDDD

Video Solution

Step-by-Step Solution

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:

CB×AD2 \frac{CB\times AD}{2}

8×92=722=36 \frac{8\times9}{2}=\frac{72}{2}=36

Answer

36 cm²

Exercise #3

The trapezoid ABCD is shown below.

AB = 2.5 cm

DC = 4 cm

Height (h) = 6 cm

Calculate the area of the trapezoid.

2.52.52.5444h=6h=6h=6AAABBBCCCDDD

Video Solution

Step-by-Step Solution

First, let's remind ourselves of the formula for the area of a trapezoid:

A=(Base + Base) h2 A=\frac{\left(Base\text{ }+\text{ Base}\right)\text{ h}}{2}

We substitute the given values into the formula:

(2.5+4)*6 =
6.5*6=
39/2 = 
19.5

Answer

1912 19\frac{1}{2}

Exercise #4

The trapezoid ABCD is shown below.

Base AB = 6 cm

Base DC = 10 cm

Height (h) = 5 cm

Calculate the area of the trapezoid.

666101010h=5h=5h=5AAABBBCCCDDD

Video Solution

Step-by-Step Solution

First, we need to remind ourselves of how to work out the area of a trapezoid:

Formula for calculating trapezoid area

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

Answer

40 cm²

Exercise #5

What is the area of the triangle in the drawing?

5557778.68.68.6

Video Solution

Step-by-Step Solution

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

5×72=352=17.5 \frac{5\times7}{2}=\frac{35}{2}=17.5

Answer

17.5

Exercise #6

Given the trapezoid:

999121212555AAABBBCCCDDDEEE

What is the area?

Video Solution

Step-by-Step Solution

Formula for the area of a trapezoid:

(base+base)2×altura \frac{(base+base)}{2}\times altura

We substitute the data into the formula and solve:

9+122×5=212×5=1052=52.5 \frac{9+12}{2}\times5=\frac{21}{2}\times5=\frac{105}{2}=52.5

Answer

52.5

Exercise #7

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

Video Solution

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

Exercise #8

Given the following rectangle:

111111777AAABBBDDDCCC

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:

11×7=77 11\times7=77

Answer

77

Exercise #9

Given the following rectangle:

222555AAABBBDDDCCC

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:

2×5=10 2\times5=10

Answer

10

Exercise #10

Given the following rectangle:

888444AAABBBDDDCCC

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:

4×8=32 4\times8=32

Answer

32

Exercise #11

Look at the rectangle ABCD below.

Given in cm:

AB = 10

BC = 5

Calculate the area of the rectangle.

101010555AAABBBCCCDDD

Video Solution

Step-by-Step Solution

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

AB×BC=10×5=50 AB\times BC=10\times5=50

Answer

50

Exercise #12

ABCD is a rectangle.

Given in cm:

AB = 7

BC = 5

Calculate the area of the rectangle.

777555AAABBBCCCDDD

Video Solution

Step-by-Step Solution

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

AB×BC=7×5=35 AB\times BC=7\times5=35

Answer

35

Exercise #13

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

Video Solution

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

Exercise #14

Calculate the area of the following triangle:

444555AAABBBCCCEEE

Video Solution

Step-by-Step Solution

The formula for calculating the area of a triangle is:

(the side * the height from the side down to the base) /2

That is:

BC×AE2 \frac{BC\times AE}{2}

We insert the existing data as shown below:

4×52=202=10 \frac{4\times5}{2}=\frac{20}{2}=10

Answer

10

Exercise #15

Calculate the area of the following triangle:

666777AAABBBCCCEEE

Video Solution

Step-by-Step Solution

The formula for the area of a triangle is

A=hbase2 A = \frac{h\cdot base}{2}

Let's insert the available data into the formula:

(7*6)/2 =

42/2 =

21

Answer

21