Area of a Rectangle - Examples, Exercises and Solutions

Question Types:
Area of a Deltoid: Applying the formulaArea of a Deltoid: Calculate The Missing Side based on the formulaArea of a Deltoid: Calculation using percentagesArea of a Deltoid: Finding Area based off Perimeter and Vice VersaArea of a Deltoid: Identifying and defining elementsArea of a Deltoid: Subtraction or addition to a larger shapeArea of a Deltoid: Using additional geometric shapesArea of a Deltoid: Using external heightArea of a Deltoid: Using Pythagoras' theoremArea of a Deltoid: Using ratios for calculationArea of a Deltoid: Using variablesArea of a Deltoid: Verifying whether or not the formula is applicableArea 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

How do we calculate the area of complex shapes?

When students hear the words "compound shapes", they usually feel uncomfortable. Just before you also ask yourself: "Oh, why this again?", know that there is no real reason. Describing shapes as compound doesn't really make them so, and it turns out that calculating areas and perimeters of compound shapes can actually be easier.

Complex shapes will be integrated into your homework and later in tests, only after you learn various shapes in geometry studies. The reason these shapes are complex is only because they are a slightly different type from those you've come to know. In each complex shape, additional shapes that you need to identify are "hiding". Dividing the complex shape into several different (and familiar) shapes will allow you to answer the question of how to calculate the area of complex shapes?

The trick: extract a familiar shape from within the complex shape

So how do we answer the question of how to calculate the area of complex shapes? First, you need to identify familiar shapes within the complex shape. An example of this: a rectangle. As you know, each shape has properties that you are familiar with, so within the complex shape itself, you can apply the properties of the familiar shape and thus calculate areas and perimeters.

After completing the missing data (according to the properties of each shape, for example: rectangle), you can complete the "puzzle", identify additional data that is revealed to you, and thus calculate the area of the complex shape. When calculating the area of complex shapes, you will often need to perform simple arithmetic operations such as division and addition (mainly for sides in the shape) - all based on the unique properties of each shape.

Practice Area of a Rectangle

Examples with solutions for Area of a Rectangle

Exercise #1

Calculate the area of the trapezoid.

555141414666

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 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 #3

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

101010777AAABBBCCCDDDEEE

Video Solution

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

Exercise #4

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 #5

Calculate the area of the triangle below, if possible.

8.58.58.5777

Video Solution

Step-by-Step Solution

The formula to calculate the area of a triangle is:

(side * height corresponding to the side) / 2

Note that in the triangle provided to us, we have the length of the side but not the height.

That is, we do not have enough data to perform the calculation.

Answer

Cannot be calculated

Exercise #6

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 #7

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

Video Solution

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

Exercise #8

The width of a rectangle is equal to 15 cm and its length is 3 cm.

Calculate the area of the rectangle.

Video Solution

Step-by-Step Solution

To calculate the area of the rectangle, we multiply the length by the width:

15×3=45 15\times3=45

Answer

45

Exercise #9

Look at the deltoid in the figure:

555666

What is its area?

Video Solution

Step-by-Step Solution

To solve the exercise, we first need to know the formula for calculating the area of a kite:

It's also important to know that a concave kite, like the one in the question, has one of its diagonals outside the shape, but it's still its diagonal.

Let's now substitute the data from the question into the formula:

(6*5)/2=
30/2=
15

Answer

15

Exercise #10

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 #11

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 #12

Given the following rectangle:

666999AAABBBDDDCCC

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

9×6=54 9\times6=54

Answer

54

Exercise #13

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 #14

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 #15

ACBD is a deltoid.

AD = AB

CA = CB

Given in cm:

AB = 6

CD = 10

Calculate the area of the deltoid.

666101010AAACCCBBBDDD

Video Solution

Step-by-Step Solution

To solve the exercise, we first need to remember how to calculate the area of a rhombus:

(diagonal * diagonal) divided by 2

Let's plug in the data we have from the question

10*6=60

60/2=30

And that's the solution!

Answer

30

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