Area Of Trapezium Questions And Answers

Area of Trapezium Questions is a useful topic for students who want to learn geometry in a simple way. Area of Trapezium helps us find the space inside a trapezium using easy formulas and clear steps. This topic is important because it builds a strong base in maths and improves problem solving skills. Students can practise different questions to understand how the formula works in real sums.

Area of Trapezium Formula

Formula Using Parallel Sides and Height

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

Where:

a = one parallel side

b = other parallel side

h = perpendicular height between parallel sides

h = perpendicular distance between a and b

Area = (1/2) × (a + b) × h

Basic Area of Trapezium Questions

Question 1: Find the area of a trapezium with parallel sides 8 cm and 6 cm, and height 4 cm.

Given:

a = 8 cm, b = 6 cm, h = 4 cm

Area = (1/2) × (a + b) × h

     = (1/2) × (8 + 6) × 4

     = (1/2) × 14 × 4

     = (1/2) × 56

     = 28 cm²

Answer: Area = 28 cm²

Question 2: A trapezium has parallel sides 12 m and 8 m, and a height of 5 m. Find its area.

Area = (1/2) × (12 + 8) × 5

     = (1/2) × 20 × 5

     = (1/2) × 100

     = 50 m²

Answer: 50 m²

Question 3: Find the area of a trapezium with parallel sides 15 cm and 10 cm, height 6 cm.

Area = (1/2) × (15 + 10) × 6

     = (1/2) × 25 × 6

     = (1/2) × 150

     = 75 cm²

Answer: 75 cm²

Question 4: Calculate the area of a trapezium whose parallel sides are 20 cm and 14 cm, and the height is 9 cm.

Area = (1/2) × (20 + 14) × 9

     = (1/2) × 34 × 9

     = (1/2) × 306

     = 153 cm²

Answer: 153 cm²

Question 5: The area of a trapezium is 60 cm². The parallel sides are 10 cm and 8 cm. Find the height.

Given: Area = 60 cm², a = 10 cm, b = 8 cm, h = ?

Area = (1/2) × (a + b) × h

60 = (1/2) × (10 + 8) × h

60 = (1/2) × 18 × h

60 = 9h

h = 60/9

h = 6.67 cm

Answer: Height ≈ 6.67 cm

Question 6: A trapezium has area 84 m² and parallel sides 16 m and 12 m. Find the height.

84 = (1/2) × (16 + 12) × h

84 = (1/2) × 28 × h

84 = 14h

h = 84/14

h = 6 m

Answer: Height = 6 m

Question 7: The two parallel sides of a trapezium are 9 cm and 5 cm. If the area is 42 cm², find the height.

42 = (1/2) × (9 + 5) × h

42 = (1/2) × 14 × h

42 = 7h

h = 6 cm

Answer: Height = 6 cm

Question 8: Find the area when a = 7.5 cm, b = 4.5 cm, h = 8 cm.

Area = (1/2) × (7.5 + 4.5) × 8

     = (1/2) × 12 × 8

     = (1/2) × 96

     = 48 cm²

Answer: 48 cm²

Area of Trapezium Questions

Question 9: A trapezium-shaped field has parallel sides of 50 m and 30 m. The perpendicular distance between the parallel sides is 20 m. Find the area of the field. If the cost of ploughing is ₹12 per m², find the total cost.

Step 1: Find the area

Area = (1/2) × (50 + 30) × 20

     = (1/2) × 80 × 20

     = (1/2) × 1600

     = 800 m²

Step 2: Find cost

Cost = 800 × 12 = ₹9,600

Answer: Area = 800 m², Cost = ₹9,600

Question 10: A trapezium-shaped swimming pool has parallel sides of 24 m and 16 m. The perpendicular distance between them is 10 m. Find the area of the pool's surface.

Area = (1/2) × (24 + 16) × 10

     = (1/2) × 40 × 10

     = (1/2) × 400

     = 200 m²

Answer: 200 m²

Question 11: A trapezium wall section has parallel sides 5 m and 3 m, and height 4 m. Paint costs ₹50 per m². Find the cost to paint the wall.

Area = (1/2) × (5 + 3) × 4

     = (1/2) × 8 × 4

     = 16 m²

Cost = 16 × 50 = ₹800

Answer: ₹800

Question 12: A trapezium and a triangle have the same area. The triangle has base 20 cm and height 12 cm. The trapezium has parallel sides 14 cm and 6 cm. Find the height of the trapezium.

Step 1: Find triangle area

Triangle Area = (1/2) × 20 × 12 = 120 cm²

Step 2: Trapezium has same area = 120 cm²

120 = (1/2) × (14 + 6) × h

120 = (1/2) × 20 × h

120 = 10h

h = 12 cm

Answer: Height of trapezium = 12 cm

Question 13: A trapezium has the same area as a rectangle of dimensions 18 cm × 10 cm. The parallel sides of the trapezium are 24 cm and 12 cm. Find the height.

Rectangle Area = 18 × 10 = 180 cm²

180 = (1/2) × (24 + 12) × h

180 = (1/2) × 36 × h

180 = 18h

h = 10 cm

Answer: Height = 10 cm

Question 14: A trapezium has parallel sides 2 m and 1.5 m, and height 80 cm. Find the area in cm².

Step 1: Convert all to cm

a = 2 m = 200 cm

b = 1.5 m = 150 cm

h = 80 cm

Step 2: Find area

Area = (1/2) × (200 + 150) × 80

     = (1/2) × 350 × 80

     = (1/2) × 28,000

     = 14,000 cm²

Answer: 14,000 cm²

Question 15: Parallel sides of a trapezium are 600 mm and 400 mm, height is 0.5 m. Find area in m².

Convert to metres:

a = 600 mm = 0.6 m

b = 400 mm = 0.4 m

h = 0.5 m

Area = (1/2) × (0.6 + 0.4) × 0.5

     = (1/2) × 1 × 0.5

     = 0.25 m²

Answer: 0.25 m²

Question 16: The parallel sides of a trapezium are in the ratio 3:5. The height is 8 cm and area is 128 cm². Find both parallel sides.

Let parallel sides be 3x and 5x

Area = (1/2) × (3x + 5x) × 8

128 = (1/2) × 8x × 8

128 = 4x × 8

128 = 32x

x = 4

a = 3 × 4 = 12 cm

b = 5 × 4 = 20 cm

Verification: (1/2)(12+20)(8) = (1/2)(32)(8) = 128 

Answer: Parallel sides = 12 cm and 20 cm

Question 17: The area of a trapezium is 180 cm². One parallel side is twice the other. Height = 12 cm. Find the parallel sides.

Let shorter side = x

Longer side = 2x

180 = (1/2) × (x + 2x) × 12

180 = (1/2) × 3x × 12

180 = 18x

x = 10 cm

Shorter side = 10 cm

Longer side = 20 cm

Verification: (1/2)(10+20)(12) = (1/2)(30)(12) = 180

Answer: 10 cm and 20 cm

Question 18: A trapezium has parallel sides that differ by 6 cm. Height = 10 cm and area = 120 cm². Find both parallel sides.

Let smaller side = x

Larger side = x + 6

120 = (1/2) × (x + x + 6) × 10

120 = (1/2) × (2x + 6) × 10

120 = 5(2x + 6)

120 = 10x + 30

90 = 10x

x = 9 cm

Smaller side = 9 cm

Larger side = 9 + 6 = 15 cm

Verification: (1/2)(9+15)(10) = (1/2)(24)(10) = 120

Answer: 9 cm and 15 cm

Question 19: A trapezium-shaped plot has parallel sides 40 m and 30 m, height 15 m. The owner wants to: a) Find the total area b) Build a fence along the perimeter (two non-parallel sides are 12 m and 13 m each) c) The fencing costs ₹200 per metre find total fencing cost

a) Area = (1/2) × (40 + 30) × 15

        = (1/2) × 70 × 15

        = 525 m²

b) Perimeter = a + b + side1 + side2

             = 40 + 30 + 12 + 13

             = 95 m

c) Fencing cost = 95 × 200 = ₹19,000

Answers:

a) Area = 525 m²

b) Perimeter = 95 m

c) Cost = ₹19,000

Question 20: Two trapeziums form a parallelogram together. The parallelogram has base 18 cm and height 10 cm. If the two trapeziums are identical and each has parallel sides of 18 cm and 12 cm, find the height of each trapezium.

Parallelogram area = base × height = 18 × 10 = 180 cm²

Each trapezium = 180/2 = 90 cm²

90 = (1/2) × (18 + 12) × h

90 = (1/2) × 30 × h

90 = 15h

h = 6 cm

Answer: Height of each trapezium = 6 cm

Question 21: A cross-section of a river channel is trapezium-shaped. The bottom width is 8 m, the top width is 14 m, and the depth is 3 m. Find the area of cross-section. If water flows at 5 m³ per second, how much water passes in 10 seconds?

Area of cross-section = (1/2) × (8 + 14) × 3

                      = (1/2) × 22 × 3

                      = 33 m²

Volume per second = Area × velocity = 33 × 5 = 165 m³

Volume in 10 seconds = 165 × 10 = 1650 m³

Answer: Cross-section area = 33 m², Water in 10 sec = 1650 m³

Area of Trapezium MCQs

Q1: Area of trapezium with a = 10 cm, b = 6 cm, h = 4 cm is:

a) 32 cm²    b) 28 cm²    c) 40 cm²    d) 16 cm²

Answer: a) 32 cm²

Solution: (1/2)(10+6)(4) = (1/2)(16)(4) = 32

Q2: The formula for area of trapezium is:

a) (a+b) × h         b) (1/2)(a+b) × h

c) (a+b)/h           d) (a × b)/h

Answer: b) (1/2)(a+b) × h 

Q3: Parallel sides are 12 and 8, height = 5. Area =?

a) 50    b) 100    c) 25    d) 40

Answer: a) 50

Solution: (1/2)(12+8)(5) = (1/2)(20)(5) = 50

Q4: Area = 90 cm², a + b = 18 cm. Find height.

a) 8 cm    b) 10 cm    c) 12 cm    d) 5 cm

Answer: b) 10 cm

Solution: 90 = (1/2)(18)(h)

 90 = 9h

h = 10

Q5: Parallel sides are in ratio 2:3. Area = 100 cm², height = 8 cm. Larger side = ?

2x + 3x = 5x

100 = (1/2)(5x)(8) = 20x

x = 5

Larger side = 3 × 5 = 15 cm

a) 10 cm    b) 12 cm    c) 15 cm    d) 20 cm

Answer: c) 15 cm

Q6: Area of trapezium doubles when:

a) Height doubles, sides stay same

b) Both parallel sides double

c) Only one side doubles

d) Height is halved

Answer: a) When height doubles, area doubles 

Q7: A trapezium and rectangle have same area. Rectangle: 15 × 8 cm. Trapezium: sides 18 and 12 cm. Height?

Rectangle area = 120 cm²

120 = (1/2)(18+12)(h) = (1/2)(30)(h) = 15h

h = 8 cm

a) 6 cm    b) 8 cm    c) 10 cm    d) 12 cm

Answer: b) 8 cm 

Q8: The parallel sides of a trapezium are increased by 20% each, height stays same. Area increases by:

Original Area = (1/2)(a+b)(h)

New sides: 1.2a and 1.2b

New Area = (1/2)(1.2a + 1.2b)(h) = 1.2 × original

Increase = 20%

a) 10%    b) 20%    c) 40%    d) 44%

Answer: b) 20%

Q9: If both parallel sides AND height all double, area becomes:

New Area = (1/2)(2a + 2b)(2h)

= (1/2)(2)(a+b)(2h)

= 4 × original area

a) 2 times    b) 3 times    c) 4 times    d) 8 times

Answer: c) 4 times

Q10: Area = 150 cm². One parallel side = 18 cm, height = 10 cm. Other side = ?

150 = (1/2)(18 + b)(10)

150 = 5(18 + b)

30 = 18 + b

b = 12 cm

a) 10 cm    b) 12 cm    c) 15 cm    d) 8 cm

Answer: b) 12 cm

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