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?
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?
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.
Large areas such as apartments are usually measured in meters, therefore, the unit of measurement will be square meter.
On the other hand, smaller figures are generally measured in centimeters, that is, the unit of measurement for the area will be square centimeter.
Remember:
Units of measurement for the area in
Units of measurement for the area
Calculate the area of the parallelogram according to the data in the diagram.
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?
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?
ACBD is a deltoid.
AD = AB
CA = CB
Given in cm:
AB = 6
CD = 10
Calculate the area of the deltoid.
ABDC is a deltoid.
AB = BD
DC = CA
AD = 12 cm
CB = 16 cm
Calculate the area of the deltoid.
Calculate the area of the parallelogram according to the data in the diagram.
We know that ABCD is a parallelogram. According to the properties of parallelograms, each pair of opposite sides are equal and parallel.
Therefore:
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:
70
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?
We begin by multiplying side AB by side BC
We then substitute the given data and we obtain the following:
Hence the area of rectangle ABCD equals 9
9 cm²
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?
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:
Thus the area of rectangle ABCD equals 25.
25 cm²
ACBD is a deltoid.
AD = AB
CA = CB
Given in cm:
AB = 6
CD = 10
Calculate the area of the deltoid.
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!
30
ABDC is a deltoid.
AB = BD
DC = CA
AD = 12 cm
CB = 16 cm
Calculate the area of the deltoid.
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
96 cm²
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.
The trapezoid ABCD is shown below.
Base AB = 6 cm
Base DC = 10 cm
Height (h) = 5 cm
Calculate the area of the trapezoid.
The trapezoid ABCD is shown below.
AB = 2.5 cm
DC = 4 cm
Height (h) = 6 cm
Calculate the area of the trapezoid.
Look at the rectangle ABCD below.
Given in cm:
AB = 10
BC = 5
Calculate the area of the rectangle.
ABCD is a rectangle.
Given in cm:
AB = 7
BC = 5
Calculate the area of the rectangle.
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.
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:
We reduce the 8 and the 2:
Divide by 4
8 cm
The trapezoid ABCD is shown below.
Base AB = 6 cm
Base DC = 10 cm
Height (h) = 5 cm
Calculate the area of the trapezoid.
First, we need to remind ourselves of how to work out the area of a trapezoid:
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
40 cm²
The trapezoid ABCD is shown below.
AB = 2.5 cm
DC = 4 cm
Height (h) = 6 cm
Calculate the area of the trapezoid.
First, let's remind ourselves of the formula for the area of a trapezoid:
We substitute the given values into the formula:
(2.5+4)*6 =
6.5*6=
39/2 =
19.5
Look at the rectangle ABCD below.
Given in cm:
AB = 10
BC = 5
Calculate the area of the rectangle.
Let's calculate the area of the rectangle by multiplying the length by the width:
50
ABCD is a rectangle.
Given in cm:
AB = 7
BC = 5
Calculate the area of the rectangle.
Let's calculate the area of the rectangle by multiplying the length by the width:
35
Calculate the area of the triangle ABC using the data in the figure.
Calculate the area of the right triangle below:
Calculate the area of the following parallelogram:
Given that the diameter of the circle is 7 cm
What is the area?
O is the center of the circle in the diagram below.
What is its area?
Calculate the area of the triangle ABC using the data in the figure.
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:
36 cm²
Calculate the area of the right triangle below:
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:
24 cm²
Calculate the area of the following parallelogram:
To solve the exercise, we need to remember the formula for the area of a parallelogram:
Side * Height perpendicular to the side
In the diagram, although it's not presented in the way we're familiar with, we are given the two essential pieces of information:
Side = 6
Height = 5
Let's now substitute these values into the formula and calculate to get the answer:
6 * 5 = 30
30 cm²
Given that the diameter of the circle is 7 cm
What is the area?
First we need the formula for the area of a circle:
In the question, we are given the diameter of the circle, but we still need the radius.
It is known that the radius is actually half of the diameter, therefore:
We substitute the value into the formula.
cm².
O is the center of the circle in the diagram below.
What is its area?
Remember that the formula for the area of a circle is
πR²
We insert the known data:
π3²
π9
cm²