Area of Rectangle Practice Problems and Polygon Areas

Master rectangle area calculations and polygon area problems with step-by-step practice. Learn formulas, solve complex shapes, and build confidence in geometry.

📚What You'll Master in This Practice Session
  • Calculate rectangle areas using the width × length formula
  • Solve complex polygon area problems by dividing shapes into rectangles
  • Apply the completion method to find areas of irregular polygons
  • Master triangle, parallelogram, and trapezoid area calculations
  • Combine multiple polygon areas to solve composite shape problems
  • Use proper units and measurements in area calculations

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

ABCD is a rectangle.

Given in cm:

AB = 7

BC = 5

Calculate the area of the rectangle.

777555AAABBBCCCDDD

Examples with solutions for Areas of Polygons for 7th Grade

Step-by-step solutions included
Exercise #1

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

101010777AAABBBCCCDDDEEE

Step-by-Step Solution

We know that ABCD is a parallelogram. According to the properties of parallelograms, each pair of opposite sides are equal and parallel.

Therefore: CD=AB=10 CD=AB=10

We will calculate the area of the parallelogram using the formula of side multiplied by the height drawn from that side, so the area of the parallelogram is equal to:

SABCD=10×7=70cm2 S_{ABCD}=10\times7=70cm^2

Answer:

70

Video Solution
Exercise #2

Calculate the area of the right triangle below:

101010666888AAACCCBBB

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

Video Solution
Exercise #3

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

121212888999AAABBBCCCDDD

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

Video Solution
Exercise #4

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

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}

Video Solution
Exercise #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.

666101010h=5h=5h=5AAABBBCCCDDD

Step-by-Step Solution

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

(Base+Base)h2=Area \frac{(Base+Base)\cdot h}{2}=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

Video Solution

Frequently Asked Questions

What is the formula for calculating the area of a rectangle?

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The area of a rectangle is calculated using the formula: Area = width × length (or A = w × h). Simply multiply the rectangle's width by its length to find the total area in square units.

How do you find the area of complex polygons that aren't standard shapes?

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There are two main methods: 1) Divide the complex polygon into familiar shapes like rectangles and triangles, calculate each area separately, then add them together. 2) Complete the shape into a larger familiar polygon, then subtract the added area to get the original area.

What's the difference between area formulas for different polygons?

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Each polygon has its specific formula: Rectangle (width × length), Triangle (base × height ÷ 2), Parallelogram (base × height), and Trapezoid ((base₁ + base₂) × height ÷ 2). The key is identifying the shape correctly first.

How do you solve area problems with composite shapes made of rectangles?

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Step 1: Identify how to divide the composite shape into individual rectangles. Step 2: Find the dimensions of each rectangle from the given measurements. Step 3: Calculate each rectangle's area using length × width. Step 4: Add all individual areas together for the total area.

What units should I use when calculating polygon areas?

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Area is always measured in square units. If your measurements are in centimeters, the area will be in square centimeters (cm²). If in meters, then square meters (m²). Always include the proper square unit notation in your final answer.

Why do triangle and trapezoid area formulas include division by 2?

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These shapes can be thought of as half of a parallelogram or rectangle. A triangle is half of a parallelogram with the same base and height. A trapezoid's formula averages the two parallel bases, creating an equivalent rectangle, which is then divided by 2 to account for the slanted sides.

What are common mistakes students make when calculating rectangle areas?

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Common errors include: mixing up length and width (though it doesn't affect the answer), forgetting to include square units, adding instead of multiplying dimensions, and incorrectly reading measurements from diagrams. Always double-check your multiplication and units.

How can I check if my polygon area calculation is correct?

+
Verification methods include: 1) Re-divide the shape differently and recalculate, 2) Estimate the area by comparing to known shapes, 3) Check that your answer makes sense given the dimensions, 4) Ensure all measurements use the same units, and 5) Verify your arithmetic by working backwards.

More Areas of Polygons for 7th Grade Questions

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Practice by Question Type

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