Trapeze - Examples, Exercises and Solutions

Understanding Trapeze

Complete explanation with examples

Types of trapezoids

Properties of a regular trapezoid
• A quadrilateral with only 2 parallel sides.
• Angles resting on the same leg are supplementary to 180 degrees, so the sum of all angles is 360 degrees.
• The diagonal of the trapezoid creates equal alternate angles between parallel lines.

Properties of a trapezoid that is a parallelogram
• A quadrilateral with 2 pairs of parallel sides – parallel bases and parallel legs.
• Its opposite sides are equal.
• Its opposite angles are equal.
• The diagonals bisect each other.

Properties of an Isosceles Trapezoid
• A quadrilateral with one pair of parallel sides and another pair of non-parallel but equal sides.
• The base angles are equal.
• The diagonals are equal.

Properties of a Right-Angled Trapezoid
• A quadrilateral with only one pair of parallel sides and 2 angles each equal to 90 degrees.
• The height of the trapezoid is the leg on which the two right angles rest.
• The other 2 angles add up to 180 degrees.

Types of Trapezoids
Detailed explanation

Practice Trapeze

Test your knowledge with 20 quizzes

Do isosceles trapezoids have two pairs of parallel sides?

Examples with solutions for Trapeze

Step-by-step solutions included
Exercise #1

Given the trapezoid:

999121212555AAABBBCCCDDDEEE

What is the area?

Step-by-Step Solution

Formula for the area of a trapezoid:

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

We substitute the data into the formula and solve:

9+122×5=212×5=1052=52.5 \frac{9+12}{2}\times5=\frac{21}{2}\times5=\frac{105}{2}=52.5

Answer:

52.5

Video Solution
Exercise #2

Look at the trapezoid in the diagram.

101010777121212777

What is its perimeter?

Step-by-Step Solution

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!

Answer:

36

Video Solution
Exercise #3

Given the trapezoid:

444999666131313

What is its perimeter?

Step-by-Step 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 4
  • Second side: 9 9
  • Third side: 6 6
  • Fourth side: 13 13

According to the formula for the perimeter of a trapezoid:

P=a+b+c+d P = a + b + c + d

Substituting the respective values:

P=4+9+6+13 P = 4 + 9 + 6 + 13

Calculating the sum, we find:

P=32 P = 32

Thus, the perimeter of the trapezoid is 32 32 .

Answer:

32

Video Solution
Exercise #4

The trapezoid ABCD is shown below.

Base AB = 6 cm

Base DC = 10 cm

Height (h) = 5 cm

Calculate the area of the trapezoid.

666101010h=5h=5h=5AAABBBCCCDDD

Step-by-Step Solution

First, we need to remind ourselves of how to work out the area of a trapezoid:

Formula for calculating trapezoid area

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

Answer:

40 cm²

Video Solution
Exercise #5

The trapezoid ABCD is shown below.

AB = 2.5 cm

DC = 4 cm

Height (h) = 6 cm

Calculate the area of the trapezoid.

2.52.52.5444h=6h=6h=6AAABBBCCCDDD

Step-by-Step Solution

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

A=(Base + Base) h2 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

Answer:

1912 19\frac{1}{2}

Video Solution

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