Area - Examples, Exercises and Solutions

Question Types:
Area of a Circle: Applying the formulaArea of a Circle: A shape consisting of several shapes (requiring the same formula)Area of a Circle: Calculate The Missing Side based on the formulaArea of a Circle: Calculating parts of the circleArea of a Circle: Finding Area based off Perimeter and Vice VersaArea of a Circle: Increasing a specific element by addition of.....or multiplication by.......Area of a Circle: Subtraction or addition to a larger shapeArea of a Circle: Using additional geometric shapesArea of a Circle: Using Pythagoras' theoremArea 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 Rhombus: Applying the formulaArea of a Rhombus: Calculate The Missing Side based on the formulaArea of a Rhombus: Calculation using percentagesArea of a Rhombus: Extended distributive lawArea of a Rhombus: Finding Area based off Perimeter and Vice VersaArea of a Rhombus: Using Pythagoras' theoremArea of a Rhombus: Using ratios for calculationArea of a Rhombus: Using variablesArea of a Rhombus: Verifying whether or not the formula is applicableArea 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 problemsArea of the Square: Applying the formulaArea of the Square: Calculate The Missing Side based on the formulaArea of the Square: Express usingArea of the Square: Increasing a specific element by addition of.....or multiplication by.......Area of the Square: True / falseArea of the Square: Worded problems

In this article, we will learn what area is, and understand how it is calculated for each shape, in the most practical and simple way there is.
Shall we start?

What is the area?

Area is the definition of the size of something. In mathematics, which is precisely what interests us now, it refers to the size of some figure.
In everyday life, you have surely heard about area in relation to the surface of an apartment, plot of land, etc.
In fact, when they ask what the surface area of your apartment is, they are asking about its size and, instead of answering with words like "big" or "small" we can calculate its area and express it with units of measure. In this way, we can compare different sizes.

Units of measurement of area

Large areas such as apartments are usually measured in meters, therefore, the unit of measurement will be m2 m^2 square meter.
On the other hand, smaller figures are generally measured in centimeters, that is, the unit of measurement for the area will be cm2 cm^2 square centimeter.
Remember:
Units of measurement for the area in cm=>cm2 cm => cm^2
Units of measurement for the area m=>m2 m=>m^2

Detailed explanation

Suggested Topics to Practice in Advance

  1. Square

Practice Area

Question 1

Calculate the area of the right triangle below:

101010666888AAACCCBBB

Question 2

Calculate the area of the trapezoid.

555141414666

Question 3

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

101010777AAABBBCCCDDDEEE

Question 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

Question 5

Calculate the area of the triangle below, if possible.

8.58.58.5777

Examples with solutions for Area

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 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 #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

Question 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

Question 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

Question 3

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

Calculate the area of the rectangle.

Question 4

O is the center of the circle in the diagram below.

What is its area?

333OOO

Question 5

Look at the deltoid in the figure:

555666

What is its area?

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

O is the center of the circle in the diagram below.

What is its area?

333OOO

Video Solution

Step-by-Step Solution

Remember that the formula for the area of a circle is

πR²

 

We insert the known data:

π3²

π9

 

Answer

9π 9\pi cm²

Exercise #10

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

Question 1

Given the following rectangle:

111111777AAABBBDDDCCC

Find the area of the rectangle.

Question 2

Given the following rectangle:

222555AAABBBDDDCCC

Find the area of the rectangle.

Question 3

Given the following rectangle:

666999AAABBBDDDCCC

Find the area of the rectangle.

Question 4

Look at the square below:

555

What is the area of the square equivalent to?

Question 5

Given the following rectangle:

888444AAABBBDDDCCC

Find the area of the rectangle.

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:

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 #14

Look at the square below:

555

What is the area of the square equivalent to?

Video Solution

Step-by-Step Solution

The area of a square is equal to the square of its side length.

In other words:

S=a2 S=a^2

Since in the diagram we are given one side of the square, and in a square all sides are equal to each other, we will solve for the area of the square as follows:

S=52=25 S=5^2=25

Answer

25 25

Exercise #15

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

More Questions

Topics learned in later sections

  1. Area of a square