Parallelogram MCQ Quiz - Objective Question with Answer for Parallelogram - Download Free PDF
Last updated on Jun 6, 2025
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.
Answer (Detailed Solution Below)
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?
Answer (Detailed Solution Below)
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?
Answer (Detailed Solution Below)
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:
Answer (Detailed Solution Below)
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.
Answer (Detailed Solution Below)
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:
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.
Answer (Detailed Solution Below)
Parallelogram Question 6 Detailed Solution
Download Solution PDFGiven
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
Answer (Detailed Solution Below)
Parallelogram Question 7 Detailed Solution
Download Solution PDFGiven:
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:
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.
Answer (Detailed Solution Below)
Parallelogram Question 8 Detailed Solution
Download Solution PDFAccording 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,
∵ 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:
Answer (Detailed Solution Below)
Parallelogram Question 9 Detailed Solution
Download Solution PDFLet 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?
Answer (Detailed Solution Below)
Parallelogram Question 10 Detailed Solution
Download Solution PDFGiven:
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?
Answer (Detailed Solution Below)
Parallelogram Question 11 Detailed Solution
Download Solution PDFGiven 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:
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?
Answer (Detailed Solution Below)
Parallelogram Question 12 Detailed Solution
Download Solution PDFGiven:
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
Answer (Detailed Solution Below)
Parallelogram Question 13 Detailed Solution
Download Solution PDFGiven:
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?
Answer (Detailed Solution Below)
Parallelogram Question 14 Detailed Solution
Download Solution PDFGiven:
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.
Answer (Detailed Solution Below)
Parallelogram Question 15 Detailed Solution
Download Solution PDFGIVEN:
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