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

Given:

Parallel sides: a = 48 cm, b = 20 cm

Non-parallel sides: c = 26 cm, d = 30 cm

Formula used:

Area of trapezium = ½ × (a + b) × height (h)

Height (h) found using: h = √(c² - m²), where m = ((a - b)² + c² - d²) / (2 × (a - b))

Calculations:

a - b = 48 - 20 = 28

m = [28² + 26² - 30²] / (2 × 28)

m = (784 + 676 - 900) / 56 = (560) / 56 = 10

h = √(26² - 10²) = √(676 - 100) = √576 = 24 cm

Area = ½ × (48 + 20) × 24 = ½ × 68 × 24 = 34 × 24 = 816 cm²

∴ Area of the trapezium = 816 cm².

Given:

Area of the trapezium = 105 sq.m

Length of the first parallel side = 9 m

Length of the second parallel side = 12 m

Formula Used:

Area of the trapezium = 1/2 × (sum of parallel sides) × height

Calculation:

Let the height of the trapezium be h meters.

Using the area formula of a trapezium:

105 = 1/2 × (9 + 12) × h

⇒ 105 = 1/2 × 21 × h

⇒ 105 = 10.5 × h

⇒ h = 105 / 10.5

⇒ h = 10

The height of the trapezium is 10 m.

Given:

The area of a trapezium = 80 cm²

The lengths of the parallel sides are 13.5 cm and 6.5 cm

Formula used:

Area of a trapezium = \(\dfrac{1}{2} \times (a + b) \times h \)

Where,

a = length of one parallel side

b = length of the other parallel side

h = height (distance between the parallel sides)

Calculation:

80 = \(\dfrac{1}{2} \times (13.5 + 6.5) \times h \)

⇒ 80 = \(\dfrac{1}{2} \times 20 \times h \)

⇒ 80 = 10h

⇒ h = \(\dfrac{80}{10}\)

⇒ h = 8 cm

∴ The correct answer is option (4).

Given:

Area of trapezium (A) = 480 cm²

Distance between parallel sides (h) = 15 cm

One parallel side (a) = 20 cm

Formula used:

A = 1/2 × (a + b) × h

Where, b = other parallel side

Calculation:

480 = 1/2 × (20 + b) × 15

⇒ 480 = 150 + 7.5b

⇒ 480 - 150 = 7.5b

⇒ 330 = 7.5b

⇒ b = 44 cm

∴ The correct answer is option (3).

Given:

​In a trapezium, one diagonal divides the other in the ratio 2 ∶ 7.

The length of the larger of the two parallel sides is 42 cm.

Concept used:

When two triangles are similar, their corresponding angles are equal and their corresponding sides are proportional.

Calculation:

According to the question,

BD divides AC in a 2 : 7 ratio. 

So, AE/EC = 2/7

BC = 42

Since AD and BC are parallel to each other, ΔAED and ΔCEB are similar triangles.

​According to the concept,

AE/CE = AD/BC

⇒ 2/7 = AD/42

⇒ AD = (42 × 2)/7

⇒ AD = 12

∴ The length of the other parallel side is 12 cm.

∴ Option 3 is the correct answer.

Area of the Trapezium = 1/2 × (Sum of the parallel sides) × (Distance between parallel sides)

⇒ 1/2 × (53 + 68) × 16

⇒ 1/2 × 121 × 16

∴ Area of the Trapezium = 968 cm²

From the above figure Using Pythagoras theorem in triangle AOB

⇒ AB² = BO² + OA²

⇒ 5² = 3² + OA²

⇒ OA = 4cm Which is equivalent to the height of the trapezium

⇒ Area = 1/2 × (height) × (sum of parallel sides)

⇒ Area = 1/2 × 4 × (8 + 14) = 44

∴ The area is 44 cm²

From the given figure,

From ΔBEF, we get

⇒ BF² = BE² + EF²

⇒ 13² = 12² + EF²

⇒ EF² = 13² – 12² = 169 – 144 = 25

⇒ EF = 5 cm

From the figure,

⇒ CD = EF = 5 cm and AB = DE = 15 cm

⇒ CF = CD + DE + EF = 5 + 15 + 5 = 25 cm

Area of the trapezoidal = ½ × BE × (AB + CF) = ½ × 12 (15 + 25) = 240 sq.cm

Given

ABCD is a trapezium such that AB = CD, AD || BC AD = 7 cm and BC = 11 cm.

area of trapezium ABCD is 54 sq.cm. 

Concept used

Area of trapezium = 1/2 (a + b) h

Calculation

Area of Trapezium = 54 cm²

1/2 (AD + BC) × h = 54

1/2 × 18 × h = 54

h = 6 cm

In Δ ABM and Δ DNC

AB = DC (given)

BM = NC 

BM + NC = 11 - 7 = 4 cm

BM = NC = 2 

IN Δ CDN

DN² + CN² = DC²

36 + 4 = DC²

DC = 2√10 cm

Formula Used:

Area of trapezium = \(\frac{1}{2}\)( sum of parallel sides )× Altitude

Area of trapezium = \(\frac{1}{2}\)( a + b ) × h

Calculation: 

Area of trapezium = \(\frac{1}{2}\)( a + b ) × h

⇒ 480 = \(\frac{1}{2}\)(20 + b ) × 15

⇒ \(​​\frac{480\times 2}{15}\) = 20 + b

⇒  64 = 20 + b

⇒ b = 64 - 20 = 44 m

∴ Correct option is 44 m.

Given:

L₁ = 17 cm

L₂ = 15 cm

Height (H) = 6 cm

Concept used:

Area of trapezium = (1/2) × (Sum of parallel side) × Height 

1 cm = (1/100) m 

Calculation:

Let two parallel side be L1 and L2

Area of trapezium = (1/2) × (17 + 15) × 6

⇒ 96 cm²

⇒ 96/10000 m² = 0.0096 m²

∴ The area of the trapezium is 0.0096 m².

Shortcut Trick Area of trapezium = (1/2) × (17 + 15) × 6

⇒ 96 cm2

= 0.0096 m2

In ∆ ADE and ∆ ABC

∠A = ∠A (common)

∠ADE = ∠ABC (corresponding)

∴ ∆ADE ~ ∆ABC

∴ (AD/AB)² = ar ∆ADE/ar ∆ABC

⇒ ar ∆ADE/ar ∆ABC = (5/11)² = 25/121

Area of trapezium DEBC = Area of ∆ABC – Area of ∆ADE = 121 – 25 = 96

∴ Area of ∆ABC : Area of trapezium DEBC = 121 : 96

Given:

Distance between parallel sides(h) = 10 cm

Sum of parallel sides(l) = 22.4 + 23.6 =46 cm

Formula used:

Area of trapezium = \(\dfrac{1}{2}× l× h\)

Calculation:

Area of trapezium = \(\dfrac{1}{2}× l× h\)

⇒ \(\dfrac{1}{2}\) × 46 × 10

⇒ 230 cm²

∴The answer is 230 cm² .

Given:

Distance between the parallel sides = 14 cm,

Length of the parallel sides are 20 cm and 25 cm.

Concept Used:

Area of trapezium = (1/2) × Sum f the parallel sides × Perpendicular distance between the parallel sides

Calculation:

According to the Question, We have:

Area of trapezium = (1/2) × Sum f the parallel sides × Perpendicular distance between the parallel sides

Area = (1/2) × (20 + 25) × 14

Area = 45 × 7

Area = 315 cm²

∴ The Area of the trapezium is 315 cm².