Area of Trapezium Questions

Area of trapezium questions are provided here with detailed solutions for students to understand how to calculate the area of the trapezium in different scenarios. These questions will help you analyse and solve various trapezium questions and enhance your skills in geometry. In this article, you will learn about finding the area of trapezium and trapezium-shaped objects using a simple formula, along with techniques for identifying the suitable approach to solve problems related to the area of trapezium.

What is the area of the trapezium?

In geometry, the trapezium is the quadrilateral with exactly one pair of parallel sides, and the other sides are called non-parallel sides or legs. However, the area of the trapezium is the amount of region covered in the two-dimensional plane.

Area of trapezium = (½) × Sum of parallel sides × Distance between parallel sides

Hare, Area = (½) × (AB + CD) × h, where h is the height or distance between the parallel sides.

Also,

Perimeter of trapezium = Sum of all the sides

Get more information about the area of trapezium here.

Area of Trapezium Questions and Answers

1. Find the area, in square metres, of the trapezium whose bases are 28 cm and 3 dm, and altitude is 25 cm.

Solution:

Given,

Length of bases of trapezium: 28 cm and 3 dm

So, the length of bases in m: 0.28 m and 0.3 m {since 10 dm = 1 m}

Length of altitude = 25 cm = 0.25 m

Area of trapezium = 1/2 (Sum of lengths of parallel sides) × altitude

= 1/2 (0.28 + 0.3) × 0.25

= 1/2 × 0.58× 0.25 = 0.0725

Therefore, the area of the trapezium (in square metres) = 0.0725

2. If the area of a trapezium with a base of 15 cm and height of 8 cm is 96 cm², find the measure of the side parallel to the given base.

Solution:

Given,

Base of the trapezium = 15 cm

Height (distance between parallel sides) = 8 cm

Let x be the measure of the side parallel to the base.

Area of trapezium = (½) × Sum of parallel sides × Distance between parallel sides

(1/2) × (15 + x) × 8 = 96 cm² (given)

15 + x = 96/4

15 + x = 24

x = 24 – 15 = 9

Therefore, the measure of the side parallel to the given base is 9 cm.

3. Calculate the area of the trapezium given in the figure.

Solution:

Given,

Length of parallel sides: 7 cm and 9 cm

Distance between parallel sides (height) = 4 cm

Area of trapezium = (½) × Sum of parallel sides × Distance between parallel sides

= (½) × (7 + 9) × 4

= 16 × 2

= 32

Hence, the area of the given trapezium is 32 cm².

4. Find the area of the given figure as the sum of the areas of two trapezia and a rectangle.

Solution:

Given,

Given that,

Length of rectangle = 50 cm

Breadth of rectangle = 10 cm

Length of parallel sides of trapezium: 30 cm and 10 cm

Distance between parallel sides of trapezium = (70 – 50)/2 = 20/2 = 10 cm

So, Distance between parallel sides of trapezium = 10 cm

Area of figure = Area of two trapeziums + Area of rectangle

Area of figure = 2 × 1/2 (Sum of lengths of parallel sides) × altitude + (Length × Breadth)

= 2 × 1/2 × (30 + 10) × 10 + (50 × 10)

= 40 × 10 + 50 × 10

= 400 + 500 = 900

Therefore, the area of the figure is 900 cm²

5. The area of a trapezium-shaped field is 30 m^2, and the distance between its parallel sides is 6 m. Find the measure of parallel sides of the field if the difference in their measurements is 2 m.

Solution:

Let x and (x + 2) be the measures of parallel sides of a trapezium.

Given,

Distance between two parallel sides = 6 m

Area of a trapezium = (½) × Sum of parallel sides × Distance between parallel sides

(½) × (x + x + 2) × 6 = 30 m² (given)

2x + 2 = 30/3

2x + 2 = 10

2x = 10 – 2 = 8

x = 8/2 = 4 m

So, x + 2 = 4 + 2 = 6 m

Hence, the measures of the two parallel sides of the trapezium field are 4 m and 6 m.

6. If the area of a trapezium is 220 cm² and the measures of parallel sides are 6 cm and 4 cm, respectively, then find the height of the trapezium.

Solution:

Let h be the height or distance between the parallel sides of a trapezium.

Given,

Measures of the parallel sides: 6 cm and 4 cm

Area of a trapezium = (½) × Sum of parallel sides × Distance between parallel sides

(½) × (6 + 4) × h = 220 cm² (given)

(½) × 10 × h = 220

h = (220 × 2)/10

h = 44

Therefore, the height of the trapezium is 44 cm.

7. Mohan wants to buy a trapezium-shaped field. Its side along the river is parallel and twice the side along the road. If the area of this field is 10500 m² and the perpendicular distance between the two parallel sides is 100 m, find the length of the side along the river.

Solution:

Let x be the length of the side of the trapezium-shaped field along the road (in m).

And let 2x be another side of the trapezium-shaped field along the road (in m).

Given,

Area of trapezium = 10500 cm²

Distance between parallel sides = 100 m

Area of trapezium = 1/2 (Sum of lengths of parallel sides) × distance between parallel sides

10500 = 1/2 (x + 2x) × 100

10500 = 1/2 (3x) × 100

3x = 10500/50

3x = 210

x = 210/3 = 70

x = 70

∴ Length of the side of trapezium shaped field along road = 70 m

Length of other side of trapezium shaped field along road = 2x = 70 × 2 = 140 m

8. The top surface of a table is a trapezium in shape. Find its area if its parallel sides are 1 m and 1.2 m and the perpendicular distance between them is 0.8 m.

Solution:

Given,

Lengths of parallel sides of the trapezium are 1.2 m and 1 m.

Distance between parallel sides = 0.8 m

Area of trapezium = (½) × (Sum of lengths of parallel sides) × Distance between parallel sides

= (½) × (1.2 + 1) × 0.8

= (½) × 2.2 × 0.8 = 0.88

= 0.88m²

Therefore, the surface area of the tabletop is 0.88 m².

9. The cross-section of the canal is in a trapezium shape, and the width of the canal at the top is 12 m, whereas 8 m at the bottom. Find the canal’s depth if the cross-section’s area is 840 m².

Solution:

Let the top and bottom widths of the canal as the parallel sides of the trapezium.

So, the lengths of parallel sides are 12 m and 8 m.

Let h be the canal’s depth (or distance between the parallel sides).

Given that the area of the cross-section is 840 m².

So, the Area of the trapezium = (½) × (Sum of lengths of parallel sides) × Distance between parallel sides

(½) × (12 + 8) × Depth of the canal = 840

(½) × 20 × h = 840

h = 84

Therefore, the depth of the canal is 84 m.

10. The parallel sides of a trapezium are in the ratio 2 : 5, and the distance between them is 10 cm. If the area of the trapezium is 350 cm², what are the parallel sides of the trapezium?

Solution:

Given,

The ratio of parallel sides of a trapezium = 2 : 5

Distance between parallel sides = 10 cm

Area of the trapezium = 350 cm²

Let 2x and 5x be the lengths of parallel sides.

So, the area of trapezium = (½) × (Sum of lengths of parallel sides) × Distance between parallel sides

(½) × (2x + 5x) × 10 = 350

7x = (350 × 2)/10

7x = 70

x = 70/7 = 10

So, 2x = 2(10) = 20

5x = 5(10) = 50

Therefore, the lengths of parallel sides of the trapezium are 20 cm and 50 cm, respectively.

Practice Questions on Area of Trapezium

1. The lengths of two parallel sides of a trapezium are 17 cm and 9 cm, respectively, and the distance between them is 7 cm. Compute the area of the trapezium.
2. The area of a trapezium is 1586 square units, and the distance between the parallel sides is 26 units. If one of the parallel sides is 38 units, find the other.\
3. ABCD is a trapezium in which AB ∥ DC, AB = 78 cm, CD = 52 cm, AD = 28 cm and BC = 30 cm. Calculate the area of the trapezium.
4. The area of a trapezium is 405 cm², and its parallel sides are in the ratio 4 : 5. If the distance between parallel sides is 18 cm, calculate the length of each of the parallel sides.
5. The parallel sides of a trapezium are 25 cm and 11 cm, while its nonparallel sides are 15 cm and 13 cm. Find the area of the trapezium.