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

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).

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).

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.

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.

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).

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

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:

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

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,

∵ 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

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

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.

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:

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.

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.

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.

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

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