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.
Calculate the area of the trapezoid.
Given the trapezoid:
What is the area?
What is the perimeter of the trapezoid in the figure?
Look at the trapezoid in the diagram.
What is its perimeter?
Below is an isosceles trapezoid
If \( ∢D=50° \)
Determine the value of \( ∢B \)?
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.
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
What is the perimeter of the trapezoid in the figure?
To find the perimeter we will add all the sides:
24
Look at the trapezoid in the diagram.
What is its perimeter?
In order to calculate the perimeter of the trapezoid we must add together the measurements of all of its sides:
7+10+7+12 =
36
And that's the solution!
36
Below is an isosceles trapezoid
If
Determine the value of ?
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: \( ∢C=2x \)
\( ∢A=120° \)
isosceles trapezoid.
Find x.
True OR False:
In all isosceles trapezoids the base Angles are equal.
Do isosceles trapezoids have two pairs of parallel sides?
What is the area of the trapezoid in the figure?
The trapezoid ABCD is shown below.
Base AB = 6 cm
Base DC = 10 cm
Height (h) = 5 cm
Calculate the area of the trapezoid.
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 base Angles are equal.
True: in every isosceles trapezoid the base angles are equal to each other.
True
Do isosceles trapezoids have two pairs of parallel sides?
To solve this problem, we'll follow these steps:
Now, let's work through each step:
Step 1: A trapezoid is defined as a quadrilateral with at least one pair of parallel sides.
Step 2: An isosceles trapezoid is a special type of trapezoid where the non-parallel sides (legs) are of equal length. Its defining feature is having exactly one pair of parallel sides, which is the same characteristic as a general trapezoid.
Step 3: Since the definition of a trapezoid inherently allows for only one pair of parallel sides, an isosceles trapezoid, as a type of trapezoid, cannot have two pairs of parallel sides. A quadrilateral with two pairs of parallel sides is typically designated as a parallelogram, not a trapezoid.
Therefore, the solution to the problem is that isosceles trapezoids do not have two pairs of parallel sides. No.
No
What is the area of the trapezoid in the figure?
We use the following formula to calculate the area of a trapezoid: (base+base) multiplied by the height divided by 2:
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.
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.
Given the trapezoid in front of you:
Given h=9, DC=15.
Since the area of the trapezoid ABCD is equal to 126.
Find the length of the side AB.
Look at the trapezoid in the figure.
The long base is 1.5 times longer than the short base.
Find the perimeter of the trapezoid.
The perimeter of the trapezoid in the diagram is 25 cm. Calculate the missing side.
In an isosceles trapezoid ABCD
\( ∢B=3x \)
\( ∢D=x \)
Calculate the size of angle \( ∢B \).
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 the trapezoid in front of you:
Given h=9, DC=15.
Since the area of the trapezoid ABCD is equal to 126.
Find the length of the side AB.
We use the formula to calculate the area: (base+base) times the height divided by 2
We input the data we are given:
We multiply the equation by 2:
We divide the two sections by 9
13
Look at the trapezoid in the figure.
The long base is 1.5 times longer than the short base.
Find the perimeter of the trapezoid.
First, we calculate the long base from the existing data:
Multiply the short base by 1.5:
Now we will add up all the sides to find the perimeter:
17.5
The perimeter of the trapezoid in the diagram is 25 cm. Calculate the missing side.
We replace the data in the formula to find the perimeter:
cm
In an isosceles trapezoid ABCD
Calculate the size of angle .
To answer the question, we must know an important rule about isosceles trapezoids:
The sum of the angles that define each of the trapezoidal sides (not the bases) is equal to 180
Therefore:
∢B+∢D=180
3X+X=180
4X=180
X=45
It's important to remember that this is still not the solution, because we were asked for angle B,
Therefore:
3*45 = 135
And this is the solution!
135°