Parallelogram MCQ Quiz - Objective Question with Answer for Parallelogram - Download Free PDF

Last updated on Jun 6, 2025

In this MCQ quiz, there are several varieties of Parallelogram Question Answers which are based on the formula of area of trapezium. These questions range from easy to difficult to provide better scope for candidates. Speed and accuracy is a must when it comes to competitive exams. Parallelogram Objective Questions will help the candidates gain both in just a brief span of time. Start practising the Parallelogram Question Answers today and learn the concepts faster.

Latest Parallelogram MCQ Objective Questions

Parallelogram Question 1:

One side of a parallelogram is 24 cm and the corresponding altitude is 6 cm. Find the area of the parallelogram.

  1. 144 cm2
  2. 120cm2
  3. 12 cm2
  4. 30 cm2

Answer (Detailed Solution Below)

Option 1 : 144 cm2

Parallelogram Question 1 Detailed Solution

Given:

One side of a parallelogram = 24 cm

Corresponding altitude = 6 cm

Formula used:

Area of a parallelogram = Base × Height

Calculations:

Area = 24 × 6

⇒ Area = 144 cm2

∴ The correct answer is option (1).

Parallelogram Question 2:

A parallelogram has a base of 12 cm and a height of 5 cm. What is the area of the parallelogram?

  1. 24 cm2
  2. 60 cm2
  3. 48 cm2
  4. 18 cm2

Answer (Detailed Solution Below)

Option 2 : 60 cm2

Parallelogram Question 2 Detailed Solution

Given:

Base (b) = 12 cm

Height (h) = 5 cm

Formula used:

Area of a parallelogram = Base × Height

Calculation:

Area = b × h

⇒ Area = 12 × 5

⇒ Area = 60 cm2

∴ The correct answer is option (2).

Parallelogram Question 3:

A flooring tile has the shape of a parallelogram whose base is 24 cm and the corresponding height is 10 cm. How many such tiles are required to cover a floor of area 1080 sq. m2?

  1. 38000
  2. 45000
  3. 42000
  4. 30000

Answer (Detailed Solution Below)

Option 2 : 45000

Parallelogram Question 3 Detailed Solution

Given:

Base of the parallelogram tile = 24 cm

Height of the parallelogram tile = 10 cm

Area to be covered = 1080 sq. m2

Formula Used:

Area of a parallelogram = Base × Height

Number of tiles required = Total area to be covered / Area of one tile

1 m2 = 10000 cm2

Calculation:

Area of one tile = 24 cm × 10 cm

⇒ Area of one tile = 240 cm2

⇒ Area of one tile = 240 / 10000 m2

⇒ Area of one tile = 0.024 m2

Number of tiles required = 1080 m2 / 0.024 m2

⇒ Number of tiles required = 45000

The correct answer is option 2.

Parallelogram Question 4:

In a parallelogram two adjacent sides are in the ratio 2 : 3 and the perimeter is 60 cm. The length of each of the two shorter sides of this parallelogram is: 

  1. 18 cm
  2. 13 cm
  3. 19 cm
  4. 12 cm

Answer (Detailed Solution Below)

Option 4 : 12 cm

Parallelogram Question 4 Detailed Solution

Given:

Two adjacent sides of a parallelogram are in the ratio 2:3

Perimeter = 60 cm

Formula used:

Perimeter of a parallelogram = 2(a + b)

Where, a and b are the lengths of the adjacent sides

Calculation:

Let the adjacent sides be 2x and 3x

Perimeter = 2(2x + 3x)

60 = 2(5x)

⇒ 60 = 10x

⇒ x = 6

Length of the shorter side = 2x = 2 × 6 = 12 cm

∴ The correct answer is option 4.

Parallelogram Question 5:

In a parallelogram ABCD, the length of the line joining the midpoints of AD and AC is 2 units. If the perimeter of the parallelogram is 26 units, then find the length of AD.

  1. 4 units
  2. 8 units
  3. 6 units
  4. 9 units

Answer (Detailed Solution Below)

Option 4 : 9 units

Parallelogram Question 5 Detailed Solution

Given:

In a parallelogram ABCD, the length of the line joining the midpoints of AD and AC is 2 units.

The perimeter of the parallelogram is 26 units.

Formula used:

The line joining the midpoints of two sides of a triangle is parallel to the third side and half its length.

Perimeter of parallelogram = 2(AB + AD)

Calculation:

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Let AD = x units and AB = y units.

Since the line joining the midpoints of AD and AC is half the length of AB, we have:

\( \frac{y}{2} = 2 \)

⇒ y = 4 units

Perimeter of parallelogram = 2(AB + AD) = 26 units

⇒ 2(x + 4) = 26

⇒ x + 4 = 13

⇒ x = 9 units

∴ The correct answer is option (4).

Top Parallelogram MCQ Objective Questions

The perimeter of a parallelogram is 48 cm. If the height of the parallelogram is 6 cm and the length of the adjacent side is 8 cm, find its area.

  1. 90 cm2
  2. 80 cm2
  3. 84 cm2
  4. 96 cm2

Answer (Detailed Solution Below)

Option 4 : 96 cm2

Parallelogram Question 6 Detailed Solution

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Given

The perimeter of a parallelogram is 48 cm.

The height of the parallelogram is 6 cm and the length of the adjacent side is 8 cm

Formula used

The perimeter of a parallelogram = 2 (adjacent side + base)

Area of a parallelogram = base × height

Calculation

According to the formula:

⇒ 48 = 2 (8 + base)

Base = 24 - 8 = 16

Area = 6 × 16 = 96 cm2  

The answer is 96 cm2

Two adjacent sides of a parallelogram are 74 cm and 40 cm, If one of its diagonals is 102 cm, then area of the parallelogram is

  1. 618 sq.cm
  2. 1224 sq.cm
  3. 2448 sq.cm
  4. 1242 sq.cm

Answer (Detailed Solution Below)

Option 3 : 2448 sq.cm

Parallelogram Question 7 Detailed Solution

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Given:

Adjacent sides of a parallelogram are 74 cm and 40 cm

One diagonal of parallelogram is 102 cm.

Formula used:

Area of parallelogram = 2 × area of a triangle that is made by a diagonal.

If a triangle has sides a, b and c respectively.

Then, By Heron's formula 

Area of triangle = \({\sqrt{s(s - a)(s - b)(s - c)}}\) where 's' is the semi-perimeter of the triangle

⇒ s = (a + b + c)/2

Calculation:

F1 Abhishek Ravi 01.11.2021 D3

Let ABCD be the given parallelogram.

Here, AB = CD = 74 cm and AD = BC = 40 cm

And, the diagonal AC = 102 cm

Now, In ΔACD

⇒ Semi-perimeter = s = (74 + 40 + 102)/2

⇒ s = 216/2 = 108

Now, area of ΔACD

⇒ \({\sqrt{108(108 - 74)(108 - 40)(108 - 102)}}\)

⇒ \({\sqrt{108 × 34 × 68 × 6}}\)

⇒ \({\sqrt{36 × 3 × 34 × 34 × 2 × 3 × 2}}\) = 6 × 3 × 34 × 2

⇒ 1224 sq. cm

Now, area of parallelogram = 2 × area of Δ ACD

⇒ 2 × 1224 = 2448 sq. cm

∴ The area of the parallelogram is 2448 sq. cm.

Important PointsProperties of parallelogram are:

  • Number of sides = 4
  • Number of vertices = 4
  • Mutually Parallel sides = 2 (in pair)
  • Area = Base x Height
  • Perimeter = 2 × (Sum of adjacent sides length)
  • Type of polygon = Quadrilateral

The lengths of the diagonals of a parallelogram are 10√3 cm and 10√2 cm. If one side of the parallelogram is 13 cm, find the perimeter of the parallelogram.

  1. 28 cm
  2. 32 cm
  3. 36 cm
  4. 44 cm

Answer (Detailed Solution Below)

Option 4 : 44 cm

Parallelogram Question 8 Detailed Solution

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According to the parallelogram law, sum of the squares of the sides equals the sum of the squares of its diagonals, i.e., for a parallelogram ABCD shown below,

F2 Vipul Pallavi 9.12.19 D3

∵ AB = CD and BC = AD, we get,

⇒ 2(AB)2 + 2(BC)2 = (AC)2 + (BD)2

Let the length of the other side of the parallelogram be ‘x’ cm

Hence, for the given parallelogram, we can write,

⇒ 2(13)2 + 2(x)2 = (10√3)2 + (10√2)2

⇒ 338 + 2x2 = 300 + 200

⇒ 2x2 = 500 – 338 = 162

⇒ x2 = 162/2 = 81

⇒ x = 9 cm

∴ Perimeter of the parallelogram = 2(13 + 9) = 44 cm

A parallelogram PQRS, the length of whose sides are 8cm and 12 cm, has one diagonal 10 cm long. The length of the other diagonal is approximately:

  1. 17.8 cm
  2. 17.5 cm
  3. 17 cm
  4. 18 cm

Answer (Detailed Solution Below)

Option 1 : 17.8 cm

Parallelogram Question 9 Detailed Solution

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Let the length of the other diagonal = x cm

In a parallelogram,

(d1)2 + (d2)2 = 2(a2 + b2)     (where d1, d2 are diagonals of the parallelogram and a & b are the sides of a parallelogram)

According to the question,

⇒ x2 + 102 = 2(82 + 122)

⇒ x2 + 100 = 2(64 + 144)

⇒ x2 = 2 × 208 – 100

⇒ x2 = 316

⇒ x = 17.8

∴ The length of the other diagonal is approximately 17.8 cm

The length of each of a pair of opposite sides of a parallelogram is 16 cm and the perpendicular distance between these two sides is 10 cm. What is the area (in cm) of the parallelogram?

  1. 80
  2. 40
  3. 160
  4. 320

Answer (Detailed Solution Below)

Option 3 : 160

Parallelogram Question 10 Detailed Solution

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Given:

The length of each a pair of opposite sides of a parallelogram is 16 cm

The perpendicular distance between these two sides is 10 cm

Concept used:

Area of a parallelogram = Base × Height (perpendicular distance between parallel sides)

Calculation:

Area of the parallelogram

⇒ 16 × 10

⇒ 160 cm2

∴ The area of the parallelogram is 160 cm2.

The two adjacent sides of a parallelogram are 12 cm and 5 cm respectively. If one of the diagonals is 13 cm long, then what is the area of the parallelogram?

  1. 60 cm2
  2. 30 cm2
  3. 75 cm2
  4. 25 cm2

Answer (Detailed Solution Below)

Option 1 : 60 cm2

Parallelogram Question 11 Detailed Solution

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Given Data:

Two adjacent sides: 12 cm and 5 cm

One diagonal: 13 cm

Concept Used:

Area of a parallelogram: Area = base × height.

Every rectangle is a parallelogram.

Calculation:

F1 SSC Savita 29-9-23 D1

Use Pythagoras in the triangle formed by sides and diagonal:

122 + 52 = 132

Since these sides are Triples, so it form the right angle triangle.

So length = 12 and height = 5

So, this is only possible in a rectangle, as every rectangle is a parallelogram, not every parallelogram is a rectangle.

⇒ Area of parallelogram: 12 × 5 = 60 cm2

Therefore, the area of the parallelogram is 60 cm2.

PQRS is a parallelogram in which PQ is 11 cm, QR is 13 cm, and PR is 16 cm. What is the difference of the lengths of the diagonals?

  1. 1 cm
  2. 2 cm
  3. 3 cm
  4. 4 cm

Answer (Detailed Solution Below)

Option 2 : 2 cm

Parallelogram Question 12 Detailed Solution

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Given:

Adjacent sides = 11 cm, 13 cm

Diagonal = 16 cm

Concept:

The sum of squares of the diagonals of a parallelogram is equal to twice the sum of the square of the sides.

Calculation:

(d12 + d22) = 2(a2 + b2)

⇒ (162 + d22) = 2 (112 + 132)

⇒ d2 = √(242 + 338 - 256)

⇒ d2 = √ 324 = 18 cm

required difference = 18 - 16 = 2 cm

∴ The difference is 2 cm.

The area of parallelogram whose base is 12 cm and whose corresponding height is 45 cm, in sq cm is

  1. 54
  2. 540
  3. 270
  4. 2700

Answer (Detailed Solution Below)

Option 2 : 540

Parallelogram Question 13 Detailed Solution

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Given:

The base of the parallelogram is 12 cm and its corresponding height is 45 cm

Concept Used:

Area of parallelogram = Base × Height

Calculation:

The base of the parallelogram is 12 cm and height is 45 cm

Area of the parallelogram is (12 × 45) cm2

⇒ 540 cm2

∴ The area of the parallelogram in sq cm is 540 cm2.

The lengths of two sides of a parallelogram are 3 cm and 10 cm. What is the sum of the squares of the diagonals of the parallelogram?

  1. 218 cm2
  2. 109 cm2
  3. 169 cm2
  4. 206 cm2

Answer (Detailed Solution Below)

Option 1 : 218 cm2

Parallelogram Question 14 Detailed Solution

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Given:

First side of parallelogram = 3 cm

Second side of parallelogram = 10 cm

Concept used:

The sum of the squares of the diagonals of a parallelogram is equal to the sum of squares of its sides

Calculations:

Let the parallelogram be ABCD,

AB = 3 cm

BC = 10 cm

CD = 3 cm

DA = 10 cm

Using the concept,

The sum of the squares of the diagonals = (AB2 + BC2 + CD2 + DA2)

⇒ (32 + 102 + 32 + 102)

⇒ (9 + 100 + 9 + 100)

⇒ 218

∴ The sum of the squares of the diagonals of the parallelogram is 218 cm2

The base of a parallelogram is twice its height. If the area of the parallelogram is 72 cm2. Find its height.

  1. 8 cm
  2. 10 cm
  3. 12 cm
  4. 6 cm

Answer (Detailed Solution Below)

Option 4 : 6 cm

Parallelogram Question 15 Detailed Solution

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GIVEN:

area of the parallelogram is 72cm2

FORMULA USED:

Area of parallelogram = (Base × Height) sq. unit

CALCULATION:

Let the height of the parallelogram be x cm  and the Base be 2x cm

⇒ Area of parallelogram = (Base × Height) sq. unit

⇒ 72 = x × 2x

⇒ 72 = 2x2

⇒ x2 = 36

⇒ x = 6

∴ Height of the parallelogram is 6 cm

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