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?", you should be aware that there is no real reason. Describing shapes as compound doesn't really make them so. As it turns out calculating areas and perimeters of compound shapes is in fact relatively straightforward.

You will be introduced to Complex shapes only after you learn various shapes in geometry. The reason these shapes are complex is due to the fact that they are slightly different from those you've come to know. In each complex shape, additional shapes that you need to identify are hidden. 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 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

ABDC is a deltoid.

AB = BD

DC = CA

AD = 12 cm

CB = 16 cm

Calculate the area of the deltoid.

161616121212CCCAAABBBDDD

Video Solution

Step-by-Step Solution

First, let's recall the formula for the area of a rhombus:

(Diagonal 1 * Diagonal 2) divided by 2

Now we will substitute the known data into the formula, giving us the answer:

(12*16)/2
192/2=
96

Answer

96 cm²

Exercise #3

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 #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

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 #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

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 #6

Shown below is the deltoid ABCD.

The diagonal AC is 8 cm long.

The area of the deltoid is 32 cm².

Calculate the diagonal DB.

S=32S=32S=32888AAABBBCCCDDD

Video Solution

Step-by-Step Solution

First, we recall the formula for the area of a kite: multiply the lengths of the diagonals by each other and divide the product by 2.

We substitute the known data into the formula:

 8DB2=32 \frac{8\cdot DB}{2}=32

We reduce the 8 and the 2:

4DB=32 4DB=32

Divide by 4

DB=8 DB=8

Answer

8 cm

Exercise #7

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 #8

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 #9

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 #10

Look at the deltoid in the figure:

777444

What is its area?

Video Solution

Step-by-Step Solution

Let's begin by reminding ourselves of the formula for the area of a kite

Diagonal1×Diagonal22 \frac{Diagonal1\times Diagonal2}{2}

Both these values are given to us in the figure thus we can insert them directly into the formula:

(4*7)/2

28/2

14

Answer

14

Exercise #11

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 #12

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 #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

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 #15

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

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