Formula for Area of Trapezium

Q.

There is a pentagon shaped park as shown in the figure. For finding its area Jyoti and Kavita divided it in two different ways,

Find the area of the above figure using either Jyothi's diagram or kavitha's diagram.

1. Area = $837.5m^2$

2. Area = $307.5m^2$

3. Area = $537.5m^2$

4. Area = $337.5m^2$

Q.

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

1. $0.88m^2$

2. $1.1m^2$

3. $6m^2$

4. $1.88m^2$

Q.

Question 8

Pragya wrapped a cord around a circular pipe of radius 4 cm (adjoining figure) and cut off the length required of the cord. Then she wrapped it around a square box of side 4 cm (also shown) Did she have any cord left?
$(Take\pi =3.14)$

Q.

The parallel sides of a trapezium are 25 cm and 11 cm, the perpendicular distance between the parallel sides is 13 cm. Find the area of the trapezium.

1. 180 cm²

2. 150 cm²

3. 234 cm²

4. Data insufficient

Q.

Which of the following has the formula $\frac{1}{2}$ {(sum of parallel sides) × h} for area ?

1. Area of rectangle

2. Area of rhombus

3. Area of square

4. Area of trapezium

Q.

The length of the parallel sides of a trapezium are in the ratio 3: 2 and the distance between them is 10 cm. If the area of the trapezium is 325 cm², find the length of the parallel sides.

1. 20cm , 40cm

2. 26 cm , 39 cm

3. 19 cm , 41 cm

4. 22 cm , 36 cm

Q. If 'a' and 'b' are the parallel sides of the trapezium and 'h' is the distance between the parallel sides, then the area of trapezium is .

1. (a+b) x h
   
2. $\frac{1}{2}$(a+b) x h
3. $\frac{1}{2}$ (a b h)

Q.

Question 95

Find the area enclosed by the following figure:

Q. The lengths of the parallel sides of a trapezium are 30 cm and 10 cm, and the distance between them is 20 cm. What is its area?

1. $400c{m}^2$
2. $360c{m}^2$
3. $480c{m}^2$
4. $280c{m}^2$

Q.

The perimeter of a trapezium is 52 cm and its each non-parallel side is equal to 10 cm with its height 8 cm. Its area is

1. $124c{m}^2$

2. $118c{m}^2$

3. $128c{m}^2$

4. $112c{m}^2$

Q.

ABCD is a trapezium. P is the midpoint of BC. AB = 12 cm, DC = 8 cm. The distance between AB and CD is 6 cm. Find the area of the triangle AQD.

1. 100 square cm.

2. 60 square cm.

3. 90 square cm.

4. 120 square cm.

Q.

Find the area of the figure given below.

1. h sq.units

2. h(a+b)sq. units

3. 2h(a+b) sq.units

4. Can't be determined

Q.

The area of an isosceles trapezium is $34c{m}^2$ and the length of one of the parallel sides is 10 cm and Its height is 4 cm. Find the length of the other parallel side.

1. 10 cm.

2. 4 cm.

3. 7 cm.

4. 9 cm.

Q.

Diagram of the adjacent picture frame has outer dimensions = 24 cm $\times$ 28 cm and inner dimensions 16 cm $\times$ 20 cm. Find the area of Section BEFC of the frame, if the width of each section is same.

1. 96 Square cm.

2. 59 Square cm.

3. 58 square cm.

4. 90 square cm.

Q.

Draw the image of Delhi Iron pillar(shape frustum) whose actual dimensions are height = 8m, base radius = 2m and top radius = 1m. [4 MARKS]

Q.

Find the area of the irregular polygon shaped fields given below.

$\left[5\right]$

Q.

The areas of figure 1 (in $c{m}^2$​) and figure 2 (in $c{m}^2$​) are __ and __ respectively.

1. $21c{m}^2$, $21c{m}^2$

2. $11c{m}^2$, $10c{m}^2$

3. $41c{m}^2$, $41c{m}^2$

4. $31c{m}^2$, $35c{m}^2$

Q.

Find the area of a trapezium if the distance between its parallel sides is 26 cm and one of the parallel sides is 84 cm, the other parallel side is half of the perpendicular distance between the parallel sides.

1. 1430 $c{m}^2$​

2. 1261 $c{m}^2$​

3. 1225 $c{m}^2$​

4. Data insufficient

Q.

Length of the fence of a trapezium-shaped field ABCD is 120 m. If BC = 48 m, CD = 17 m and AD = 40 m, find the area of this field, given that side AB is perpendicular to the parallel sides AD and BC.

1. $600m^2$

2. $260m^2$

3. $640m^2$

4. $660m^2$

Q.

The larger trapezium is made up of the four smaller trapeziums which are equal in size. If FD = 48 cm, then, select the statements that are true.

1. FE = ED

2. DC = AB

3. DC = 2AB

4. FE = 24 cm

Q.

A pond is in the shape of a trapezium. A bridge is to be constructed such that the bridge is perpendicular to the parallel sides. It is given that the area of a pond is 1080 $m^2$ and the lengths of its parallel sides are 55 m and 35 m. Find the length of the bridge.

1. 56 m

2. 24 m

3. 48 m

4. Data insufficient

Q. Find the area of the given trapezium.

1. 200 cm${}^2$
2. 202 cm${}^2$
3. 204 cm${}^2$
4. 206 cm${}^2$

Q.

Two parallel sides of a trapezium are of lengths 57 cm and 39 cm. The distance between the parallel sides is 30 cm. Find the area of the trapezium.

1. $1440c{m}^2$

2. $1244c{m}^2$

3. $1144c{m}^2$

4. $1044c{m}^2$

Q.

Question 1 (h)
State whether true or false.

(h) All squares are trapeziums.

Q.

Choose the correct statements from the following:

Statement 1: All the parallelograms having the same base and lying between the same parallels have equal areas.

Statement 2: All the parallelograms having the same base and lying between the same parallels have different perimeters.

Statement 3: Of all the parallelograms having the same base and lying between same parallels, the rectangle will have the smallest perimeter.

Statement 4: All the parallelograms having equal areas must have the same base but they may or may not lie between the same parallels.

1. 1, 2, 4

2. 1, 2

3. 1, 2, 3

4. 1, 2, 3, 4

Q.

The area of a trapezium is 1586 cm²and the distance between its parallel sides is 26 cm. If one of the parallel sides is 84 cm, then find the other parallel side.

1. 38 cm

2. 23 cm

3. 25 cm

4. Data insufficient

Q.

ABCD is a trapezium. P is the midpoint of BC. AB = 14 cm, DC = 6 cm. The distance between AB and CD is 8 cm. Find the area of the triangle AQD.

1. 10 square cm.

2. 80 square cm.

3. 90 square cm.

4. 50 square cm.

Q.

There is a regular octagonal park. Find the surface area of the park (in $m^2$ ).

1. 123

2. 119

3. 122

4. 120

Q.

There is a regular octagonal park. Find the surface area of the park (in $m^2$ ).
___

Q.

The area of a trapezium shaped field is 600 m², the distance between two parallel sides is 10 m and one of the parallel side is 20 m. Find the other parallel side.

1. $40m$

2. $50m$

3. $60m$

4. $70m$