Unlock hundreds more features
Save your Quiz to the Dashboard
View and Export Results
Use AI to Create Quizzes and Analyse Results

OR
Sign inSign in with Facebook
Sign inSign in with Google
Quizzes > High School Quizzes > Mathematics

Area Practice Quiz: Trapezoids, Triangles & Parallelograms

Practice essential worksheets for geometry area mastery

Difficulty: Moderate
Grade: Grade 6
Study OutcomesCheat Sheet
Colorful paper art promoting Shape Area Showdown, a geometry trivia quiz for middle school students.

Easy
What is the formula for the area of a triangle?
1/2 * (base + height)
base * height
1/2 * base * height
base + height
The area of a triangle is calculated by taking half the product of its base and height. This formula reflects that a triangle is essentially half of a parallelogram with the same dimensions.
What is the area of a parallelogram with a base of 5 units and a height of 3 units?
18
15
8
10
The area of a parallelogram is computed by multiplying its base by its height. With a base of 5 and a height of 3, the calculation yields an area of 15 square units.
What is the area of a trapezoid with bases measuring 4 and 6 units and a height of 5 units?
20
30
15
25
The area of a trapezoid is calculated using the formula A = 1/2 * (base1 + base2) * height. Substituting the given values, (4 + 6), halved and then multiplied by 5 gives an area of 25.
Which shape's area is given by multiplying its base and height directly?
Parallelogram
Triangle
Circle
Trapezoid
A parallelogram's area is computed simply as base multiplied by height. Unlike triangles or trapezoids, it does not require halving the product.
Which formula correctly represents the area of a trapezoid?
base1 * base2 * height
base * height
1/2 * (base1 + base2) * height
(base1 + base2) * height
The area of a trapezoid is given by half the product of the sum of its bases and its height. This formula calculates the average length of the two bases multiplied by the height.
Medium
Calculate the area of a triangle with a base of 8 cm and a height of 6 cm.
48
14
28
24
The triangle area formula is A = 1/2 * base * height. Substituting 8 cm for the base and 6 cm for the height gives (1/2)*8*6 = 24 square centimeters.
A parallelogram has an area of 30 square centimeters and a base of 5 centimeters. What is its height?
10 cm
6 cm
7 cm
5 cm
The area of a parallelogram is calculated as base multiplied by height. Dividing the area (30) by the base (5) gives a height of 6 cm.
A trapezoid has an area of 36 cm² and a height of 4 cm. If one of its bases is 5 cm, what is the sum of the bases?
16 cm
18 cm
12 cm
20 cm
Using the trapezoid area formula: A = 1/2 * (b1 + b2) * h, we rearrange to find b1 + b2 = (2*A)/h. Substituting in 36 and 4 gives (72/4) = 18 cm.
Find the height of a triangle with an area of 15 cm² and a base of 10 cm.
2 cm
3 cm
4 cm
5 cm
The triangle area formula is A = 1/2 * base * height. Rearranging gives height = (2*A)/base. Substituting 15 for the area and 10 for the base yields a height of 3 cm.
Determine the area of a parallelogram with a base of 7 cm and a height of 9 cm.
56 cm²
49 cm²
63 cm²
72 cm²
A parallelogram's area is found by multiplying its base by its height. Here, 7 cm multiplied by 9 cm gives an area of 63 square centimeters.
Choose the correct formula for calculating the area of a trapezoid with bases b1 and b2, and height h.
1/2 * (b1 + b2) * h
1/2 * (b1 * h + b2 * h)
(b1 * b2) * h
(b1 + b2) * h
The area of a trapezoid is computed as 1/2 * (b1 + b2) * h, which averages the two bases before multiplying by the height. This option is the correct representation.
If a triangle and a parallelogram share the same base and height, how do their areas compare?
The triangle's area is double that of the parallelogram
The triangle's area is one-quarter of the parallelogram's area
The triangle's area is half the parallelogram's area
They have the same area
A triangle's area is calculated as half the product of its base and height, while a parallelogram's area is the full product. Therefore, when they share the same dimensions, the triangle's area is half that of the parallelogram.
What is the area of a trapezoid with bases of 10 cm and 12 cm, and a height of 4 cm?
48 cm²
46 cm²
40 cm²
44 cm²
Using the formula A = 1/2 * (b1 + b2) * h, substituting the values gives (1/2 * (10 + 12) * 4) which equals 44 square centimeters.
If a triangle has an area of 32 cm² and a height of 8 cm, what is the length of its base?
8 cm
4 cm
10 cm
6 cm
By rearranging the triangle area formula (A = 1/2 * base * height), the base can be calculated as (2*A)/height. Substituting 32 and 8 gives a base length of 8 cm.
If a trapezoid and a parallelogram have the same height, and the average of the trapezoid's bases equals the parallelogram's base, how do their areas compare?
The trapezoid's area is one-third that of the parallelogram
The trapezoid's area is twice that of the parallelogram
The areas are equal
The trapezoid's area is half that of the parallelogram
Since the trapezoid's area formula is 1/2 * (b1 + b2) * h and the average of its bases matches the parallelogram's base, the resulting area equals base * height, which is the parallelogram's area.
Hard
A decorative garden is designed in the shape of a trapezoid adjacent to a triangle. The trapezoid has bases of 8 cm and 12 cm and a height of 5 cm, while the triangle shares the same height and has a base of 6 cm. What is the total area of the design?
55 cm²
60 cm²
70 cm²
65 cm²
The trapezoid's area is calculated as 1/2 * (8 + 12) * 5 = 50 cm², and the triangle's area is 1/2 * 6 * 5 = 15 cm². Adding these areas together yields a total of 65 cm².
A triangle has an area of 84 square units and a base of 14 units. What is its height?
12 units
14 units
16 units
10 units
Using the formula for the area of a triangle (A = 1/2 * base * height), we solve for the height by rearranging to (2*A)/base. Substituting 84 and 14 results in a height of 12 units.
The area of a parallelogram is 90 square units. If the base is increased by 50% and the height is reduced by 20%, what is the new area?
112 square units
100 square units
108 square units
96 square units
Increasing the base by 50% multiplies it by 1.5 and reducing the height by 20% multiplies it by 0.8. The new area is 1.5 * 0.8 times the original area, which is 1.2 * 90 = 108 square units.
A trapezoid has an area of 72 square centimeters with a height of 6 cm. One of its bases is 10 cm. What is the length of the other base?
18 cm
14 cm
12 cm
16 cm
Using the trapezoid area formula A = 1/2 * (b1 + b2) * h, we substitute the known values to get 72 = 1/2 * (10 + b2) * 6. Solving the equation yields the other base as 14 cm.
A composite figure consists of a parallelogram and a triangle sharing a common base of 8 cm. The parallelogram's height is 5 cm and the triangle's height is 3 cm. What is the combined area of the figure?
60 cm²
56 cm²
48 cm²
52 cm²
The parallelogram's area is calculated as base * height (8 * 5 = 40 cm²) and the triangle's area as 1/2 * base * height (1/2 * 8 * 3 = 12 cm²). The total area is therefore 40 + 12 = 52 cm².
0
{"name":"What is the formula for the area of a triangle?", "url":"https://www.quiz-maker.com/QPREVIEW","txt":"Easy, What is the formula for the area of a triangle?, What is the area of a parallelogram with a base of 5 units and a height of 3 units?","img":"https://www.quiz-maker.com/3012/images/ogquiz.png"}

Study Outcomes

  1. Calculate the area of trapezoids using the appropriate formula.
  2. Determine the area of triangles by applying basic geometric principles.
  3. Compute the area of parallelograms through variable substitutions in the formula.
  4. Analyze geometric shapes to identify relevant dimensions for area calculation.
  5. Apply problem-solving strategies to evaluate the area of various shapes accurately.

Area Worksheet: Trapezoids, Triangles & Parallelograms Cheat Sheet

  1. Master the Triangle Area Formula - Slice your study like a pizza: area = ½ × base × height turns that triangle into a tasty equation you can visualize in seconds. Remember, height means the perpendicular from base to the top vertex! BBC Bitesize: Triangle Area
    2. BBC Bitesize: Triangle Area
  2. Understand Parallelogram Areas - Think of a parallelogram as a slanted rectangle: its area is simply base × height, where height is the straight-up distance between the top and bottom edges. It's like tipping your board but keeping the same math! K5 Learning: Parallelogram Area Tips
    3. K5 Learning: Parallelogram Area Tips
  3. Calculate Trapezoid Areas with Ease - A trapezoid is just a rectangle plus half a triangle on each side: area = ½ × (base₝ + base₂) × height. Averaging the two parallel sides makes this formula a breeze! GeeksforGeeks: Trapezoid Area
    4. GeeksforGeeks: Trapezoid Area
  4. Visualize Area Formulas - Turning shapes into other shapes is key: cut and shuffle a parallelogram to make a rectangle, so base × height jumps off the page. Seeing proofs in action cements the concept! One Mathematical Cat: Area Proofs
    5. One Mathematical Cat: Area Proofs
  5. Use Mnemonics for Trapezoid Areas - Make math melodic by singing "Half the sum of the parallel sides, times the distance between them" to your favorite tune. Catchy rhythms help formulas stick in your brain! Mammoth Memory: Trapezoid Mnemonic
    6. Mammoth Memory: Trapezoid Mnemonic
  6. Practice with Real-World Problems - Apply your skills by calculating the area of a garden, a poster board, or even a slice of cake. Tackling these fun scenarios turns study into play! AnalyzeMath: Practical Area Exercises
    7. AnalyzeMath: Practical Area Exercises
  7. Recognize Shape Properties - Knowing that parallelograms have equal opposite sides and angles helps you spot the right base and height every time. This detective work ensures no sneaky slants trip you up! Wikipedia: Parallelogram Properties
    8. Wikipedia: Parallelogram Properties
  8. Break Down Complex Shapes - Chop irregular figures into triangles and parallelograms to tackle them piece by piece. It's like solving a puzzle - each piece has its area, so just add them up! One Mathematical Cat: Composite Shapes
    9. One Mathematical Cat: Composite Shapes
  9. Memorize Key Formulas - Flashcards, doodles, or catchy jingles can lock triangle, parallelogram, and trapezoid area formulas into your memory. Quick recall boosts your confidence and your test scores! One Mathematical Cat: Formula List
    10. One Mathematical Cat: Formula List
  10. Stay Positive and Practice Regularly - Every problem you solve is another victory lap for your brain! Consistency beats cramming, so keep solving, stay upbeat, and watch your math muscles grow. Khan Academy: Test Prep
    11. Khan Academy: Test Prep
Make a Quiz (FREE) Copy & Edit This Quiz Create a Quiz with AI

Mathematics Quizzes

Powered by: Quiz Maker