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Quizzes > High School Quizzes > Mathematics

Trapezoid Worksheet Practice Quiz

Master trapezoid concepts with this interactive quiz

Difficulty: Moderate
Grade: Grade 7
Study OutcomesCheat Sheet
Paper art representing a trivia quiz on trapezoid properties for high school geometry students.

Which of the following correctly defines a trapezoid in geometry?
A quadrilateral with one pair of parallel sides
A quadrilateral with no parallel sides
A quadrilateral with two pairs of parallel sides
A quadrilateral with all sides congruent
A trapezoid is defined as a quadrilateral that has exactly one pair of parallel sides. This distinguishes it from parallelograms or rectangles which have two pairs of parallel sides.
In a trapezoid, which sides are known as the bases?
The non-parallel sides
The parallel sides
The diagonals
The perpendicular segments
The bases of a trapezoid are the sides that are parallel to each other. This property is central to the identification and analysis of trapezoidal shapes.
Which formula correctly calculates the area of a trapezoid?
Area = 1/2 × (base1 + base2) × height
Area = (base1 × base2) / height
Area = (base1 × height) + (base2 × height)
Area = base1 + base2 + height
The area of a trapezoid is computed by taking half the sum of its two bases and multiplying the result by the height. This formula is a fundamental tool in solving geometric problems involving trapezoids.
What are the non-parallel sides of a trapezoid called?
Bases
Legs
Diagonals
Altitudes
The non-parallel sides of a trapezoid are known as the legs. This terminology helps distinguish them from the bases, which are the parallel sides used in area calculations.
Which statement is always true about any trapezoid?
Its diagonals are perpendicular
It must be an isosceles trapezoid
All its interior angles are right angles
It has exactly one pair of parallel sides
By definition, a trapezoid has exactly one pair of parallel sides. The other statements describe properties that are not universally applicable to all trapezoids.
Given a trapezoid with bases of 8 cm and 12 cm and a height of 5 cm, what is its area?
60 cm²
50 cm²
100 cm²
40 cm²
Using the trapezoid area formula, Area = 1/2 × (base1 + base2) × height, we calculate 1/2 × (8 + 12) × 5 = 50 cm². This demonstrates how to apply the formula with given measurements.
A trapezoid has bases of 15 cm and 9 cm and legs of equal length at 10 cm each. What type of trapezoid is this?
Right trapezoid
Isosceles trapezoid
Scalene trapezoid
Parallelogram
A trapezoid is classified as isosceles when its non-parallel sides (legs) are congruent. Since both legs here measure 10 cm, the trapezoid is isosceles.
What distinguishes an isosceles trapezoid from a general trapezoid?
It has equal base lengths
It has two pairs of parallel sides
Its non-parallel sides are congruent
Its diagonals are perpendicular
An isosceles trapezoid is specifically defined by the congruence of its legs. This additional property results in symmetrical features, such as congruent diagonals, which are not required in a general trapezoid.
If a trapezoid has an area of 84 square units, one base measuring 10 units, and a height of 6 units, what is the length of the other base?
14 units
22 units
18 units
28 units
Using the formula Area = 1/2 × (base1 + base2) × height, substitute the given values to get 84 = 1/2 × (10 + base2) × 6. Solving this equation shows that the unknown base measures 18 units.
Which property holds true for the diagonals of an isosceles trapezoid?
They are congruent
They bisect each other
They are perpendicular
They are parallel
In an isosceles trapezoid, one of its defining characteristics is that the diagonals are of equal length (congruent). This feature, however, does not extend to all trapezoids.
For a trapezoid with bases of 20 cm and 30 cm, what is the length of the midsegment?
25 cm
50 cm
10 cm
60 cm
The midsegment of a trapezoid is calculated as the average of the two bases. Thus, (20 cm + 30 cm) / 2 gives a midsegment length of 25 cm.
Which formula should be rearranged to solve for the height of a trapezoid when given its area and bases?
Area = base1 + base2 + height
Area = 1/2 × (base1 + base2) × height
Area = (base1 × base2) × height
Area = base1 × base2 / height
To find the height when the area and the base lengths are known, you start with the formula Area = 1/2 × (base1 + base2) × height. Rearranging this equation allows you to solve for the unknown height.
A trapezoid has a midsegment of 12 cm and a height of 7 cm. What is its area?
84 square units
42 square units
56 square units
96 square units
Since the midsegment of a trapezoid is the average of the bases, the area can be calculated as midsegment multiplied by the height. Here, 12 cm × 7 cm results in an area of 84 square units.
If the midsegment of a trapezoid is 8 cm long, what is the sum of the lengths of its bases?
8 cm
16 cm
20 cm
12 cm
The midsegment is defined as the average of the two bases of a trapezoid. Therefore, if the midsegment is 8 cm, the sum of the bases must be 16 cm.
How does increasing the height of a trapezoid affect its area if the bases remain constant?
It has no effect on the area
It increases the area exponentially
It increases the area linearly
It decreases the area
The area of a trapezoid is directly proportional to its height. Therefore, if the bases remain the same, any increase in height results in a linear increase in area.
A trapezoid has one base of 13 cm, an unknown base x cm, a height of 7 cm, and an area of 98 cm². What is the value of x?
10 cm
18 cm
15 cm
20 cm
Substitute the values into the trapezoid area formula: 98 = 1/2 × (13 + x) × 7. Simplifying gives (13 + x) = 28, so x = 15 cm. This illustrates how to solve for a missing base using the area formula.
In an isosceles trapezoid, if one base angle measures 60° and the altitude is 5 cm, which additional measurement is needed to calculate the length of a leg using trigonometry?
The perimeter of the trapezoid
The difference in the lengths of the bases
The length of the midsegment
The measure of the other base angle
To calculate the leg length using trigonometry, you form a right triangle using the altitude and half the difference of the bases as the horizontal leg. Thus, knowing the difference between the bases is essential.
A trapezoid has bases of 16 cm and 24 cm, and one leg makes a 45° angle with the base while measuring 10 cm. What is the height of the trapezoid?
5 cm
7.07 cm
10 cm
12 cm
Using the sine function in the right triangle formed by the leg and the height, we have height = leg × sin(45°). Thus, height = 10 × (√2/2) which is approximately 7.07 cm.
Which set of vertices, when connected in order, would form a trapezoid with exactly one pair of parallel sides?
Vertices: (1, 1), (3, 4), (6, 4), (8, 1)
Vertices: (0, 0), (4, 0), (5, 2), (1, 2)
Vertices: (0, 0), (4, 0), (3, 2), (1, 2)
Vertices: (0, 0), (3, 1), (4, 3), (1, 2)
Option A creates a quadrilateral where only the first and last pair of points form parallel lines. The other sets either form additional pairs of parallel sides or do not yield the proper configuration for a trapezoid with exactly one pair of parallel sides.
In a trapezoid, the diagonals intersect at point E. The segments created on one diagonal are proportional to which pair of sides?
The lengths of the legs
The midsegment and a leg
The lengths of the bases
The heights
A notable property of trapezoids is that the intersection of the diagonals divides them in a ratio equal to the lengths of the bases. This proportionality is specific to the bases and is useful in more advanced geometric problem solving.
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Study Outcomes

  1. Identify and describe the key properties of trapezoids, including parallel sides and angle relationships.
  2. Calculate the area and perimeter of trapezoids using standard geometric formulas.
  3. Analyze dynamic problems to determine unknown measurements within trapezoids.
  4. Apply geometric principles to solve real-world trapezoid-related challenges.

Trapezoid Worksheet Cheat Sheet

  1. Understanding a Trapezoid - A trapezoid is a quadrilateral with at least one pair of parallel sides called bases. The legs are the non‑parallel sides, which can be equal or different in length. This shape gives you the perfect base (get it?) for lots of geometry fun! Explore Trapezoid Basics
  2. Area Formula - To find the area, average the two bases, then multiply by the height and divide by two. It's like making the perfect sandwich: delicious layers (bases) and the filling (height) all contribute to the final taste (area)! Learn the Area Calculation
  3. Perimeter Calculation - The perimeter is simply the sum of all four sides: base₝ + base₂ + leg₝ + leg₂. Grab your measuring tape (or a trusty calculator) and add them up to get the total distance around your trapezoid. Perimeter Formula Guide
  4. Isosceles Trapezoid - In an isosceles trapezoid, both legs are congruent, and the base angles at each end are equal, making it extra symmetrical. Picture a fancy trapezoid wearing matching socks - both sides look just right! Properties of Isosceles Trapezoids
  5. Diagonals Equality - A cool trick of the isosceles trapezoid is that its diagonals are equal in length. That means if you draw both diagonals, they'll be perfect twins stretching across your shape. Diagonals in Action
  6. Median or Midsegment - The median (also called the midsegment) connects the midpoints of the legs and runs parallel to the bases. Its length is the average of the two bases, so it's like the trapezoid's way of being fair to both sides. Median Formula Explained
  7. Sum of Interior Angles - Just like any quadrilateral, a trapezoid's interior angles always add up to 360°. So if you know three angles, you can always find the fourth by subtracting their sum from 360°. Angle‑Sum Rule
  8. Right Trapezoid - A right trapezoid has one leg perpendicular to the bases, making two right angles at the base. Think of it as a trapezoid that decided to stand up straight on one side. Right Angle Trapezoid Guide
  9. Height (Altitude) - The height is the perpendicular distance between the two bases, often drawn as a vertical dashed line. It's the secret ingredient in area calculations, so always look for it first! Finding the Height
  10. What Are Legs? - The non‑parallel sides of a trapezoid are called legs, and they can be equal or unequal depending on the trapezoid type. These "legs" give your shape extra character - sometimes it's fancy and balanced, other times it's quirky! Learn About Trapezoid Legs
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