Trapezoid Practice Problems for 9th Grade - Area & Properties

Master trapezoid properties, area formulas, and angle calculations with step-by-step practice problems designed for ninth grade students learning quadrilaterals.

📚Master Trapezoid Concepts Through Targeted Practice
  • Calculate trapezoid area using the formula with parallel bases and height
  • Identify and classify isosceles, right angle, and standard trapezoids
  • Find missing angles in isosceles trapezoids using angle properties
  • Solve for unknown variables in trapezoid area problems
  • Apply midsegment theorem to find missing trapezoid measurements
  • Determine ratios between trapezoid segments and triangle areas

Understanding Trapezoids

Complete explanation with examples

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.

Characteristics of the Trapezoid

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.

A1 - Characteristics and types of trapezoids


Detailed explanation

Practice Trapezoids

Test your knowledge with 40 quizzes

Do isosceles trapezoids have two pairs of parallel sides?

Examples with solutions for Trapezoids

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:

(Base+Base)h2=Area \frac{(Base+Base)\cdot h}{2}=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

Frequently Asked Questions

What is the formula for finding the area of a trapezoid?

+
The area of a trapezoid is calculated using the formula: Area = (b₁ + b₂) × h ÷ 2, where b₁ and b₂ are the lengths of the parallel bases and h is the height. This formula works by finding the average of the two bases and multiplying by the height.

How do you identify different types of trapezoids?

+
There are three main types: 1) Regular trapezoid - has one pair of parallel sides, 2) Isosceles trapezoid - has equal leg lengths and equal base angles, 3) Right trapezoid - contains two right angles where the height equals one of the legs.

What are the angle properties of an isosceles trapezoid?

+
In an isosceles trapezoid, base angles are equal (angles on the same base have equal measures), and adjacent angles are supplementary (they add up to 180°). The legs are also equal in length, making it symmetric across its vertical axis.

How do you find missing angles in trapezoids?

+
Use these rules: adjacent angles on the same side add to 180°, base angles in isosceles trapezoids are equal, and the sum of all angles equals 360°. Start with known angles and apply these properties systematically.

What is a midsegment in a trapezoid and how do you calculate it?

+
A midsegment connects the midpoints of the two legs (non-parallel sides) of a trapezoid. Its length equals the average of the two parallel bases: midsegment = (base₁ + base₂) ÷ 2, and it runs parallel to both bases.

How do you solve trapezoid problems with variables?

+
Steps to follow: 1) Identify what the variable represents, 2) Set up the area formula or angle relationship, 3) Substitute known values, 4) Solve the resulting equation algebraically, 5) Check your answer by substituting back into the original problem.

What makes trapezoid problems challenging for 9th graders?

+
Students often struggle with: distinguishing between different trapezoid types, remembering that only one pair of sides is parallel, applying the correct area formula, and working with variables in geometric contexts. Practice with labeled diagrams helps overcome these challenges.

How are trapezoids different from parallelograms?

+
Key differences: Trapezoids have exactly one pair of parallel sides (bases), while parallelograms have two pairs of parallel sides. In trapezoids, only base angles may be equal (in isosceles type), whereas parallelograms have opposite angles equal and adjacent angles supplementary.

More Trapezoids Questions

Practice by Question Type

More Resources and Links