Exercise 2.2 (Area of the rhombus)

Exercise 2.2

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

(i) d₁ = 8 cm, d₂ = 16 cm

Area of the rhombus = 1/2 [ d₁ × d₂ ] 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 × d₂ = 468 sq m.

                       d₂ = 468 /13 = 36 m

(iii) 1/2 × d₁ × 12 = 180 sq.mm

                        d₁ = 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 d₁ = 8 cm

The length of other diagonal = d₂

Area of the rhombus = 1/2 × d₁ × d₂ = 100

= 1/2 × 8 × d₂ = 100

 d₂ = 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.

d₁ = 4 cm

d₂ = 5 cm

Area of the rhombus = 1/2 × d₁ × d₂ 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°