Trapezoids - Examples, Exercises and Solutions

Formula for the area of a trapezoid:

$\frac{(base+base)}{2}\times altura$

We substitute the data into the formula and solve:

$\frac{9+12}{2}\times5=\frac{21}{2}\times5=\frac{105}{2}=52.5$

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!

The problem requires calculating the perimeter of the trapezoid by summing the lengths of its sides. Based on the given trapezoid diagram, the side lengths are clearly marked as follows:

• First side: $4$
• Second side: $9$
• Third side: $6$
• Fourth side: $13$

According to the formula for the perimeter of a trapezoid:

$P = a + b + c + d$

Substituting the respective values:

$P = 4 + 9 + 6 + 13$

Calculating the sum, we find:

$P = 32$

Thus, the perimeter of the trapezoid is $32$.

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

First, let's remind ourselves of the formula for the area of a trapezoid:

$A=\frac{\left(Base\text{ }+\text{ Base}\right)\text{ h}}{2}$

We substitute the given values into the formula:

(2.5+4)*6 =
6.5*6=
39/2 = 
19.5

The formula for the area of a trapezoid is:

We are given the following dimensions:

• Base $AB = 5$ cm
• Base $DC = 9$ cm
• Height $h = 7$ cm

Substituting these values into the formula, we have:

First, add the lengths of the bases:

Now substitute back into the formula:

Calculate the multiplication:

Then multiply by the height:

Thus, the area of the trapezoid is 49 cm$^2$.

To find the perimeter we will add all the sides:

$4+5+9+6=9+9+6=18+6=24$

To find the perimeter of the trapezoid, we will sum the lengths of all its sides. The given side lengths are:

• Base 1: $7.5$
• Base 2: $1.5$
• Leg 1: $3$
• Leg 2: $4$

Using the formula for the perimeter $P$ of the trapezoid, we have:

$P = a + b + c + d$

Substituting in the given values:

$P = 7.5 + 1.5 + 3 + 4$

Performing the addition:

$P = 7.5 + 1.5 = 9$

$P = 9 + 3 = 12$

$P = 12 + 4 = 16$

Therefore, the perimeter of the trapezoid is $16$.

To solve this problem, we'll follow these steps:

• Step 1: Identify all given side lengths of the trapezoid.
• Step 2: Apply the formula for the perimeter of the trapezoid.
• Step 3: Sum up the lengths to find the perimeter.

Now, let's work through each step:
Step 1: The problem gives us the lengths of the trapezoid's sides:
- $AB = 2.5$
- $BC = 10.4$
- $CD = 5.3$
- $DA = 6$

Step 2: We use the formula for the perimeter of a trapezoid:

$P = AB + BC + CD + DA$

Step 3: Plugging in the given values, we calculate:

$P = 2.5 + 10.4 + 5.3 + 6$

Calculating further, we have:

$P = 24.2$

Therefore, the perimeter of the trapezoid is $24.2$.

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:

$A+C=180$

$B+D=180$

Since angle D is known to us, we can calculate:

$180-50=B$

$130=B$

Given that the trapezoid is isosceles and the angles on both sides are equal, it can be argued that:

$∢C=∢D$

$∢A=∢B$

We know that the sum of the angles of a quadrilateral is 360 degrees.

Therefore we can create the formula:

$∢A+∢B+∢C+∢D=360$

We replace according to the existing data:

$120+120+2x+2x=360$

 $240+4x=360$

$4x=360-240$

$4x=120$

We divide the two sections by 4:

$\frac{4x}{4}=\frac{120}{4}$

$x=30$

True: in every isosceles trapezoid the base angles are equal to each other.

To solve this problem, we'll follow these steps:

• Step 1: Define the geometric properties of a trapezoid.
• Step 2: Define the geometric properties of an isosceles trapezoid.
• Step 3: Conclude whether an isosceles trapezoid has two pairs of parallel sides based on these definitions.

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.

To determine the area of the trapezoid, we will follow these steps:

• Step 1: Identify the provided dimensions of the trapezoid.
• Step 2: Apply the formula for the area of a trapezoid.
• Step 3: Perform the arithmetic to calculate the area.

Let's proceed through these steps:

Step 1: Identify the dimensions
The given dimensions from the diagram are:
Height $h = 3$ cm.
One base $b_1 = 4$ cm.
The other base $b_2 = 7$ cm.

Step 2: Apply the area formula
To find the area $A$ of the trapezoid, use the formula:
$A = \frac{1}{2} \times (b_1 + b_2) \times h$

Step 3: Calculation
Substituting the known values into the formula:
$A = \frac{1}{2} \times (4 + 7) \times 3$

Simplify the expression:
$A = \frac{1}{2} \times 11 \times 3$

Calculate the result:
$A = \frac{1}{2} \times 33 = \frac{33}{2} = 16.5$ cm²

The area of the trapezoid is therefore $16.5$ cm².

Given the choices, this corresponds to choice : $16.5$ cm².

Therefore, the correct solution to the problem is $16.5$ cm².

To find the area of the trapezoid, we will follow these steps:

• Step 1: Identify the given dimensions of the trapezoid.
• Step 2: Apply the area formula for a trapezoid using these dimensions.
• Step 3: Perform the calculation to determine the area.

Let's work through each step more clearly:
Step 1: From the problem, we identify that the trapezoid has one base $b_1 = 13$ units, another base $b_2 = 8$ units, and its height $h = 5$ units.
Step 2: The formula for the area of a trapezoid is:

$A = \frac{1}{2} \times (b_1 + b_2) \times h$

Step 3: Substitute the values into the formula:

$A = \frac{1}{2} \times (13 + 8) \times 5$

$A = \frac{1}{2} \times 21 \times 5$

$A = \frac{1}{2} \times 105$

$A = 52.5 \, \text{units}^2$

Therefore, the area of the trapezoid is $52.5 \, \text{units}^2$.