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 right triangle below:
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 triangle ABC using the data in the figure.
The trapezoid ABCD is shown below.
AB = 2.5 cm
DC = 4 cm
Height (h) = 6 cm
Calculate the area of the trapezoid.
Given that the diameter of the circle is 7 cm
What is the area?
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
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
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
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
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.
The trapezoid ABCD is shown below.
Base AB = 6 cm
Base DC = 10 cm
Height (h) = 5 cm
Calculate the area of the trapezoid.
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.
What is the area of the triangle in the drawing?
Given the trapezoid:
What is the area?
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?
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
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
What is the area of the triangle in the drawing?
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
17.5
Given the trapezoid:
What is the area?
Formula for the area of a trapezoid:
We substitute the data into the formula and solve:
52.5
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
Look at the deltoid in the figure:
What is its area?
Given the following rectangle:
Find the area of the rectangle.
Given the following rectangle:
Find the area of the rectangle.
Given the following rectangle:
Find the area of the rectangle.
Look at the rectangle ABCD below.
Given in cm:
AB = 10
BC = 5
Calculate the area of the rectangle.
Look at the deltoid in the figure:
What is its area?
Let's begin by reminding ourselves of the formula for the area of a kite
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
14
Given the following rectangle:
Find the area of the rectangle.
Let's calculate the area of the rectangle by multiplying the length by the width:
77
Given the following rectangle:
Find the area of the rectangle.
Let's calculate the area of the rectangle by multiplying the length by the width:
10
Given the following rectangle:
Find the area of the rectangle.
Let's calculate the area of the rectangle by multiplying the length by the width:
32
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