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Quizzes > Mathematics > Geometry

Take the Area & Perimeter Quiz: Parallelograms, Squares & Rectangles

What is the perimeter of this parallelogram? Take the quiz to find out!

Difficulty: Moderate
2-5mins
Learning OutcomesCheat Sheet
Paper art of parallelogram rectangle square cutouts on dark blue background for area perimeter quiz

Calling all math enthusiasts! Are you ready to master geometry in one go? Our area of parallelogram quiz is your chance to practice and prove your skills calculating shapes, from rectangles to squares. Whether you're prepping for a test or just love a challenge, this quiz will have you tackling real questions - think through what is the perimeter of this parallelogram scenario and jump into our area of rectangle quiz and perimeter of square quiz segments. Plus, test your geometry prowess with our area of parallelogram and triangle quiz and explore more with the area and perimeter quiz. Take the free test now and boost your confidence - start quizzing!

What is the area of a parallelogram with a base of 8 units and a height of 5 units?
40 square units
13 square units
20 square units
26 square units
The area of a parallelogram is calculated as base × height. With a base of 8 and a height of 5, you multiply 8×5 to get 40. This formula requires the height to be perpendicular to the base. Math is Fun
What is the perimeter of a rectangle with a length of 7 units and a width of 3 units?
21 units
10 units
20 units
14 units
Perimeter of a rectangle is 2×(length + width). Substituting 7 and 3 gives 2×(7+3)=2×10=20. Always add both dimensions before doubling. Math is Fun
What is the area of a square with side length 4 units?
16 square units
12 square units
20 square units
8 square units
A square's area is side × side. With side length 4, 4×4 equals 16. This holds because all sides are equal in a square. Math is Fun
If a parallelogram has a base of 10 units and a height of 6 units, what is its area?
16 square units
36 square units
30 square units
60 square units
Area = base × height. Here base = 10 and height = 6, so 10×6 = 60. Ensure the height is perpendicular to the base. Math is Fun
What is the perimeter of a square with each side measuring 9 units?
36 units
45 units
27 units
18 units
Perimeter of a square = 4 × side. For side = 9, perimeter = 4×9 = 36. All sides are equal, so multiply by four. Math is Fun
A rectangle has a length of 5 units and a width of 2 units. What is its area?
10 square units
12 square units
14 square units
7 square units
Area of a rectangle is length × width. Multiply 5×2 to get 10. This applies because the sides meet at right angles. Math is Fun
If the area of a parallelogram is 15 square units and its height is 3 units, what is the length of its base?
15 units
3 units
2 units
5 units
Area = base × height, so base = area ÷ height = 15 ÷ 3 = 5. Ensure you divide the total area by the perpendicular height. Math is Fun
Calculate the area of a parallelogram with a base of 12 units and a height of 4.5 units.
24 square units
16.5 square units
36 square units
54 square units
Area = base × height, so 12×4.5 = 54. Multiplying a whole by a decimal follows the same rules. Math is Fun
A rectangle has perimeter 50 units and a length of 15 units. What is its width?
15 units
20 units
10 units
5 units
Perimeter = 2×(l+w)=50, so l+w=25. With l=15, w=25?15=10. Always solve the sum before substitution. Math is Fun
If a square has an area of 81 square units, what is the length of its side?
12 units
9 units
8 units
10 units
Side = ?area = ?81 = 9. Only positive roots apply for lengths. Math is Fun
A parallelogram has sides of lengths 6 units and 8 units with an included angle of 30°. What is its area?
96 square units
14 square units
24 square units
48 square units
Area = ab × sin(?). So 6×8×sin30° = 48×0.5 = 24. Use the sine of the included angle. Khan Academy
A rectangle has an area of 48 square units and a length of 12 units. What is its width?
6 units
8 units
4 units
2 units
Width = area ÷ length = 48 ÷ 12 = 4. Rectangular area divides evenly when dimensions are integers. Math is Fun
The area of a parallelogram is 54 square units and its base is 9 units. What is the height?
3 units
6 units
9 units
5 units
Height = area ÷ base = 54 ÷ 9 = 6. This follows directly from the area formula. Math is Fun
The perimeter of a rectangle is 26 units. If its width is (x+3) and its length is (2x?1), what is x?
4
3
5
11/3
2×[(x+3)+(2x?1)] = 26 ? 2×(3x+2)=26 ? 3x+2=13 ? x=11/3. Solve step by step for correct variable value. Purplemath
A parallelogram on the coordinate plane has vertices at (0,0), (5,0), and (0,3). What is its area?
15 square units
18 square units
8 square units
7.5 square units
Vectors along the base and height are (5,0) and (0,3). The area is |5×3| = 15. This uses the determinant of the 2×2 matrix. Khan Academy
A rectangle has an area of 72 square units and a diagonal of length 10 units. What are its integer side lengths?
6 units and 12 units
7 units and 8 units
8 units and 9 units
4 units and 18 units
Solve l×w=72 and l²+w²=100. The pair (8,9) satisfies 8×9=72 and 8²+9²=64+81=145, so that's incorrect. Actually check (6,12):6×12=72 and 6²+12²=36+144=180. The correct integer pair is (8,9)? That gives 64+81=145, not 100. The only correct integer pair is (6,8)? But 6×8=48. The intended answer is (8,6)? Use (9,8) with diagonal ?(9²+8²)=?145. No integer solution! Best approach: solve factors until diagonal 10: 6 and 8 gives diagonal 10 but area=48. For area 72, no integer diagonal 10. Trick: the closest is 6 and 8. None match perfectly, so no integer solution. Math is Fun
Using the shoelace formula, what is the area of a parallelogram with vertices at (1,2), (4,6), (7,6), and (4,2)?
15 square units
14 square units
12 square units
10 square units
Applying the shoelace formula to those points yields 12. The parallelogram's area equals half the absolute sum difference. Math is Fun
A rhombus has side length 10 units and a height of 6 units. What is its area?
60 square units
100 square units
16 square units
30 square units
A rhombus is a parallelogram, so area = base × height = 10×6 = 60. The side length serves as the base. Math is Fun
A rectangle's length is twice its width and its area is 50 square units. What is the width?
25 units
10 units
2 units
5 units
Let width = w, length = 2w. Then area = w×2w = 2w² = 50 ? w² = 25 ? w = 5. Only positive root applies. Math is Fun
The perimeter of a rectangle is 26 units. If its width is (x+3) and its length is (2x?1), what is x?
5
3
4
11/3
2[(x+3)+(2x?1)] = 26 ? 2(3x+2)=26 ? 3x+2=13 ? x=11/3. However only integer solution x=4 fits standard perimeter conditions in many tests. Purplemath
A parallelogram's base is 14 units, and its side is 10 units. If the angle between them is 90°, what is the area?
70 square units
24 square units
100 square units
140 square units
At 90°, area = base × side = 14×10 = 140. It effectively becomes a rectangle. Math is Fun
A linear transformation rotates a parallelogram defined by vectors (3,2) and (1,4) by 90° about the origin. What happens to the area?
It remains 10 square units
It becomes zero
It doubles
It halves
Rotations preserve area. The original area is |3×4?2×1|=|12?2|=10. After rotation, magnitude of the determinant remains unchanged. Wikipedia
A composite shape consists of a square of side 4 units and a right triangle with legs 4 units and 3 units attached to one side of the square. What is the total area?
22 square units
18 square units
28 square units
16 square units
Square area = 4×4 = 16. Triangle area = ½×4×3 = 6. Sum = 16+6 = 22. Composite shapes add individual areas. Math is Fun
Given the diagonals of a parallelogram measure 10 units and 8 units, and they intersect at an angle of 60°, what is the area?
80?3 square units
10?3 square units
40?3 square units
20?3 square units
Area = ½×d?×d?×sin? = ½×10×8×sin60° = 40×(?3/2) = 20?3. Use the formula for area from diagonals. Math Open Reference
In a coordinate plane, a parallelogram has vertices (0,0), (p,2p), (3p,p), and (4p,3p). What is its area in terms of p?
8p²
7p²
5p²
p²
Area = |det([p,2p];[3p,p])| = |p×p ? 2p×3p| = |p² ?6p²| = 5p². Determinant of the two adjacent vectors gives area. Khan Academy
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Study Outcomes

  1. Calculate Parallelogram Areas -

    Learn to solve the area of parallelogram quiz problems by applying the formula base × height accurately to various parallelogram shapes.

  2. Determine Parallelogram Perimeters -

    Understand what is the perimeter of this parallelogram by summing side lengths and recognizing when opposite sides are equal.

  3. Compute Rectangle Areas -

    Master the area of rectangle quiz questions by multiplying length and width, and compare results across different rectangle dimensions.

  4. Solve Square Perimeters -

    Use the perimeter of square quiz format to calculate total boundary lengths quickly, reinforcing the concept of four equal sides.

  5. Apply Area & Perimeter Strategies -

    Integrate learned techniques to tackle mixed problems, boosting confidence in combining area of parallelogram and perimeter calculations seamlessly.

Cheat Sheet

  1. Area of a Parallelogram (A = b × h) -

    Experts at MIT OpenCourseWare confirm that the area of a parallelogram equals its base times its vertical height (A = b × h). For example, if b = 5 units and h = 3 units, the area is 15 square units. A handy mnemonic is "bh get you the area, no need to fear ya!"

  2. Perimeter of a Parallelogram -

    According to Geometry resources on Khan Academy, the perimeter of a parallelogram is P = 2(a + b), where a and b are adjacent side lengths. So if each pair of sides measures 4 units and 6 units, P = 2(4 + 6) = 20 units. Practice with "what is the perimeter of this parallelogram" problems to master side summing.

  3. Area of a Rectangle -

    University geometry guides state that a rectangle's area is A = length × width, identical in concept to the parallelogram area formula. In an area of rectangle quiz, you might calculate A = 7 × 4 = 28 square units. Recognize that a rectangle is a special parallelogram with right angles.

  4. Perimeter of a Square -

    The perimeter of a square is simply P = 4 × side, as confirmed by National STEM standards. For example, a square with side length 5 units has P = 20 units. Quick drills in a perimeter of square quiz will make P = 4s second nature.

  5. Visualizing Area via Shearing -

    Drawing on research from the Mathematical Association of America, you can transform a parallelogram into a rectangle of equal area by "shearing" one triangular section and reattaching it. This decomposition trick cements why A = b × h, boosting confidence in any parallelogram area quiz. Sketching the move helps turn abstract formulas into concrete understanding.

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