Question

1. The area of the trapezium with parallel bases 2cm and 4cm and the distance between them is 3cm is ____cm² *

a. 9
b. 6
c. 7
c. 24

2. The area of a parallelogram of base 6cm and height 2cm is ____cm².

a. 8
b. 6
c. 12
d. 16

3. A rectangular wire of length 40 cm and breadth 20 cm is bent in the shape of a square. The side of the square is _____cm *

a. 10
b. 20
c. 30
d. 40

4. The area of a rhombus whose diagonals are of lengths 10 cm and 8.2 cm is ____cm² *

a. 41
b. 82
c. 410
d. 820

5. The area of a trapezium is 40 cm². Its parallel sides are 12 cm and 8 cm. The distance between the parallel sides is _____cm *

a. 1
b. 2
d. 3
c. 4​

Answer 1

Answer:

1. a)9
2. c)12
3. c)30
4. dont know
5. c)4

Answer 2

1. The area of the trapezium with parallel bases 2 cm and 4 cm and the distance between them is 3 cm is ____cm²:

a. 9 ✔

b. 6

c. 7

d. 24

Explanation:

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

Parallel side, a = 2 cm

Parallel side, b = 4 cm

Distance between them, h = 3 cm

$\sf{Area=\dfrac{1}{2}\times(2+4)\times3}$

$\sf{Area=\dfrac{1}{2}\times6\times3}$

$\sf{Area=9\:cm^2}$

2. The area of a parallelogram of base 6 cm and height 2cm is ____ cm².

a. 8

b. 6

c. 12 ✔

d. 16

Explanation:

$\sf{\implies\:Area\:of\:a\:parallelogram=bh}$

Base of the parallelogram, b = 6 cm

Height of the parallelogram, h = 2 cm

$\sf{Area=6\times2}$

$\sf{Area=12\:cm^2}$

3. A rectangular wire of length 40 cm and breadth 20 cm is bent in the shape of a square. The side of the square is _____cm.

a. 10

b. 20

c. 30 ✔

d. 40

Explanation:

$\sf{\implies\:Perimeter\:of\:a\:rectangle=2(l+b)}$

Length = 40 cm

Breadth = 20 cm

Perimeter = 2 (40 + 20)

Perimeter = 2 x 60

Perimeter = 120 cm which will be the same for the square.

$\sf{\implies\:Perimeter\:of\:a\:square=4a}$

$\sf{Given\:perimeter=120\:cm}$

$\sf{4a=120\:cm}$

$\sf{a=\dfrac{120}{4}}$

$\sf{Side=30\:cm}$

4. The area of a rhombus whose diagonals are of lengths 10 cm and 8.2 cm is ____cm².

a. 41 ✔

b. 82

c. 410

d. 820

Explanation:

$\sf{\implies\:Area\:of\:a\:rhombus=\dfrac{1}{2}d_1d_2}$

Diagonal 1 = 10 cm

Diagonal 2 = 8.2 cm

$\sf{Area=\dfrac{1}{2}\times10\times8.2}$

$\sf{Area=5\times8.2}$

$\sf{Area=41\:cm^2}$

5. The area of a trapezium is 40 cm². Its parallel sides are 12 cm and 8 cm. The distance between the parallel sides is _____cm.

a. 1

b. 2

c. 4​ ✔

d. 3

Explanation:

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

Given area = 40 cm²

Parallel side, a = 12 cm

Parallel side, b = 8 cm

$\sf{\dfrac{1}{2}\times(12+8)\times\:h=40\:cm^2}$

$\sf{\dfrac{1}{2}\times20\times\:h=40\:cm^2}$

$\sf{10h=40\:cm^2}$

$\sf{h=\dfrac{40}{10}}$

$\sf{h=4\:cm}$