The trapezoid is considered one of the most intimidating shapes for students, therefore we have decided to provide a summary of the general idea behind the trapezoid and explain its properties to them and introduce some types of trapezoids.
The trapezoid is considered one of the most intimidating shapes for students, therefore we have decided to provide a summary of the general idea behind the trapezoid and explain its properties to them and introduce some types of trapezoids.
A trapezoid is a quadrilateral based on 4 sides like any other,
but special in that it will always have two parallel sides also called bases, which we can call the larger base and the smaller base
and it will also have two opposite sides also called legs.
The trapezoid ABCD is shown below. Given in cm:
Base AB = 6
Base DC = 10
Height (h) = 5
Calculate the area of the trapezoid.
There are several types of trapezoids that you will encounter during your studies.
For example, there are trapezoids where the lines look in the same direction and it is called a parallelogram
Additionally, there is a trapezoid that has two sides of the same length and it is called an Isosceles trapezoid. In the first example, we have a right angle trapezoid, which is a trapezoid where the height is equal to the side perpendicular to the bases so that 2 right angles are formed.
How do we calculate the area of a trapezoid?
We are given the following isosceles trapezoid with the following characteristics:
Task:
What is its height?
Solution:
Formula for the area of a trapezoid:
Substituting these values into our formula we have the following:
And we solve:
Answer:
Height is equal to .
The trapezoid ABCD is shown below.
AB = 2.5 cm
DC = 4 cm
Height (h) = 6 cm
Calculate the area of the trapezoid.
The trapezoid ABCD is shown below.
AB = 5 cm
DC = 9 cm
Height (h) = 7 cm
Calculate the area of the trapezoid.
What is the perimeter of the trapezoid in the figure?
Given the area of a trapezoid where its lower base is twice the upper base and times greater than the height.
The area of the trapezoid is equal to (find help starting from )
Task:
Calculate the value of .
Solution:
Given that the lower base is twice the upper base and times larger than the height.
if we divide everything by
Now taking the square root of both sides
Answer:
Given that is an isosceles trapezoid with the following characteristics
Task:
Find the angles of the trapezoid and the angle
Solution:
The sum of adjacent angles
This is because is an isosceles triangle
Opposite the equal sides of the triangle
The sum of the adjacent angles in the trapezoid are equal to
between the two bases
Angles opposite by the vertex
Answer:
What is the perimeter of the trapezoid in the figure?
Look at the trapezoid in the figure.
Calculate its perimeter.
\( ∢D=50° \)
The isosceles trapezoid
What is \( ∢B \)?
Given that is an isosceles trapezoid
Task:
What is the midsegment opposite to in the triangle whose base is equal to?
Solution:
--->
Given the figure that:
The rule:
Opposite sides are equal in , is equal to the sides
Side =
Side =
Angle =
According to the side, side, angle congruence theorem
Corresponding sides between overlapping triangles
A midsegment in a triangle is equal to half of the side it corresponds to.
Midsegment =
Answer:
The area of the trapezoid
The line creates the triangle and the parallelogram .
It is known that the ratio of the area of the triangle to the area of the parallelogram is .
Task:
Calculate the ratio between the sides and .
Solution:
To calculate the ratio between the sides we will use the figure that:
We calculate using the formula to find half of the area and place the ratio.
To solve the equation, multiply across the factors.
Dividing everything by we have the following:
The ratio between is
Answer:
Answer:
Given: \( ∢A=120° \)
The isosceles trapezoid
Find a: \( ∢C \)
Given: \( ∢C=2x \)
\( ∢A=120° \)
isosceles trapezoid.
Find x.
True OR False:
In all isosceles trapezoids the bases are equal.
What are the characteristics of trapezoids?
The characteristics of a trapezoid are those that help us define or classify which type of trapezoid we are referring to. It's important to remember that there are different types of trapezoids, such as the isosceles trapezoid, the right trapezoid, or a parallelogram. Therefore, it is very important to take into account the characteristics of each one.
What characteristics does a right trapezoid have?
The characteristics of a right trapezoid are that it has two right angles, one acute angle, and one obtuse angle, resulting in two of its sides being equal.
What are the elements of a trapezoid?
As we have already mentioned, a trapezoid is a quadrilateral (4 sides) that has two parallel sides, which are called bases, usually considered as the larger base and the smaller base, it has a height, and it has 4 angles.
What is an isosceles trapezoid?
An isosceles trapezoid is one that has two equal sides, which are the sides that join its parallel lines. This is one of the main characteristics of this type of trapezoid.
Do isosceles trapezoids have two pairs of parallel sides?
What is the area of the trapezoid in the diagram below?
What is the area of the trapezoid in the diagram?
Calculate the area of the trapezoid.
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.
Cannot be calculated.
What is the perimeter of the trapezoid in the figure?
To find the perimeter we will add all the sides:
24
The isosceles trapezoid
What is ?
Let's recall that in an isosceles trapezoid, the sum of the two angles on each of the trapezoid's legs equals 180 degrees.
In other words:
Since angle D is known to us, we can calculate:
130°
Given:
isosceles trapezoid.
Find x.
Given that the trapezoid is isosceles and the angles on both sides are equal, it can be argued that:
We know that the sum of the angles of a quadrilateral is 360 degrees.
Therefore we can create the formula:
We replace according to the existing data:
We divide the two sections by 4:
30°
True OR False:
In all isosceles trapezoids the bases are equal.
True: in every isosceles trapezoid the base angles are equal to each other.
True