7th Maths : Term 1 Unit 2 : Measurements : Area of the rhombus : Text Book Back Exercises Questions with Answers, Solution

**Exercise 2.2**

** **

**1.
Find the area of rhombus PQRS shown in the following figures.**

(i) d_{1} = 8 *cm*,
d_{2} = 16 *cm*

Area of the rhombus = 1/2 [ d_{1} × d_{2} ] *sq.units*

= 1/2 × 8 × 16 *sq.cm*

**= 64 sq.cm**

(ii)

Base *b* = 15 *cm*

height *h *= 11 *cm*

Area of the rhombus = *b*
× * h
sq. units*

= 15 × 11 *sq.cm*

** = 165 sq.cm**

** **

**2.
Find the area of a rhombus whose base is 14 ***cm*** and height is
9 ***cm***.**

Base *b* = 14 *cm*

height *h* = 9 *cm*

Area of the rhombus = *b × h
sq.units*

= 14 × 9 *sq.cm*

** = 126 sq.cm**

** **

**3.
Find the missing value.**

(i) 1/2 × 19 × 16 = 152 *sq.cm*

(ii) 1/2 × 26 × d_{2} = 468 *sq m.*

d_{2} = 468 /13 = 36 *m*

(iii) 1/2 × d_{1} × 12~~ ~~= 180 *sq.mm*

d_{1 }= 18/6 = 30 *mm*

** **

**4.
The area of a rhombus is 100 ***sq. cm*** and length of
one of its diagonals is 8 ***cm***. Find the
length of the other diagonal.**

The area of the rhombus = 100 sq.cm

The length of one diagonal d_{1} = 8 cm

The length of other diagonal = d_{2}

Area of the rhombus = 1/2 × d_{1} × d_{2 }= 100

= 1/2 × 8 × d_{2 }= 100

d_{2} = 100/4 = 25
cm

**The length of the
other diagonal = 25 cm**

** **

**5.
A sweet is in the shape of rhombus whose diagonals are given as 4 ***cm*** and 5 ***cm***. The surface
of the sweet should be covered by an aluminum foil. Find the cost of aluminum
foil used for 400 such sweets at the rate of ****₹**** 7 per 100 ***sq. cm***.**

d_{1 }= 4 *cm *

d_{2} = 5 *cm*

Area of the rhombus = 1/2 × d_{1} × d_{2} *sq.units*

Area of the rhombus = 1/2 × ~~4~~ × 5 = 10 *sq.cm*

Area of 1 sweet = 10 *sq.cm*

Area of 400 sweets = 10 × 400 = 4000 *sq.cm*

Cost of 100 sq.cm aluminum foil = ₹ 7

∴ Cost of 4000 sq.cm aluminum foil = ₹ 7 × 4000 / 100

= ₹ 280

**The cost of a aluminum
foil used for 400 sweets = ₹ 280**

** **

__Objective
type questions__

**6. The area of the rhombus with side 4 ***cm*** and height 3 ***cm*** is**

(i)
7 *sq*. *cm*

(ii)
24 *sq*. *cm*

(iii)
12 *sq*. *cm*

(iv)
10 *sq*. *cm*

*Answer :***(iii) 12 sq.cm**

**7. The area of the rhombus when both diagonals
measuring 8 ***cm*** is**

(i)
64 *sq*. *cm*

(ii)
32 *sq*. *cm*

(iii)
30 *sq*. *cm*

(iv)
16 *sq*. *cm*

*Answer :***(ii) 32 sq.cm**

**8.
The area of the rhombus is 128 ***sq***. ***cm*** and the
length of one diagonal is 32 ***cm***. The length
of the other diagonal is**

(i) 12* cm
*

(ii) 8* cm
*

(iii) 4*
cm *

(iv) 20 *cm*

*Answer :***(ii) 8 cm**

**9.
The height of the rhombus whose area 96 sq.
m and side 24 m is**

(i) 8* m *

(ii) 10* m
*

(iii) 2* m
*

(iv) 4 *m*

*Answer :***(iv) 4 m**

**10.
The angle between the diagonals of a rhombus is **

(i) 120º

(ii) 180º

(iii) 90º

(iv) 100º

*Answer :***(iii) 90°**

**ANSWERS**

**Exercise 2.2 **

1. (i) 64* sq.cm *(ii) 165* sq.cm *

2. 126* sq.cm *

3. (i) 152* sq.cm *(ii) 36* m *(iii) 30* mm*

4. 25* cm *

5. ₹ 280

** Objective type questions **

6. (iii) 12* sq.cm *

7. (ii) 32* sq.cm *

8. (ii) 8* cm *

9. (iv) 4* cm *

10. (iii) 90°

Tags : Questions with Answers, Solution | Measurements | Term 1 Chapter 2 | 7th Maths , 7th Maths : Term 1 Unit 2 : Measurements

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7th Maths : Term 1 Unit 2 : Measurements : Exercise 2.2 (Area of the rhombus) | Questions with Answers, Solution | Measurements | Term 1 Chapter 2 | 7th Maths

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