Answer:

1) Rhombus is a special type of parallelogram and the area of a parallelogram is the product of its base and height.

Find the area of a rhombus whose side is 5 cm and whose altitude is 4.8 cm. If one of its diagonals is 8 cm long, find the length of the other diagonal

Let the length of the other diagonal of the rhombus AD be x.

Area of the rhombus ABDC = Base × Length = 5 cm × 4.8 cm = 24 cm²

Also,

Area of rhombus = 1/2 × Product of its diagonals

24 = 1/2 (AD × CB)

24 = 1/2 (x × 8 cm)

x × 4 = 24

x = 6 cm

Thus the length of the other diagonal is 6 cm

2) Let ABDC be a rhombus as shown below with AD and BC as the diagonals.

The floor of a building consists of 3000 tiles which are rhombus shaped and each of its diagonals are 45 cm and 30 cm in length. Find the total cost of polishing the floor, if the cost per m² is ₹ 4.

Let BC = 30 cm, AD = 45 cm

Area of rhombus ABDC = Area of ΔABC + Area of ΔDCB

= 1/2 × (BC × AO) + 1/2 × (BC × OD)

= 1/2 × BC × (AO + OD)

= 1/2 × BC × AD

= 1/2 × 30 cm × 45 cm

= 675 cm²

Area of each tile = 675 cm²

Area covered by 3000 tiles = (675 × 3000) cm² = 2025000 cm² = 202.5 m²

Given that the cost of polishing is Rs. 4 per m²

Cost of polishing for 202.5 m² area = Rs. 4 × 202.5 = Rs. 810

3) As the field is in trapezium shape, we will use the formula to find the area of trapezium

Let the side DC of the roadside (b₁ of trapezium) be x cm

The opposite parallel side AB (b₂ of trapezium) = 2x m

h = 100 m (given)

Area of the field = 10500 m2

Area of trapezium = 1/2 (b₁ + b₂) × h

10500 = 1/2 (2x + x) × 100

2 × 10500 = 3x × 100

21000 = 300x

x = DC = 70 m

So, AB = 2x = 2 × 70 = 140 m

Thus, the length of the field riverside = 140 m.

Answer:

The area of the rhombus with side 5 cm and altitude 4.8 cm is 24 cm2, and the length of the other diagonal is 6 cm.

Step-by-step explanation:

Let's draw the diagram of rhombus ABCD according to the given question.

Side of the rhombus = 5 cm

So, AB = BC = CD = DA = 5cm (Since all the sides of a rhombus are equal)

Area of a rhombus = Base × Height (Since, rhombus is also a parallelogram)

= 5 cm × 4.8 cm (Since, altitude = 4.8cm)

= 24 cm2

Also, 

Area of a rhombus = (Product of the digonals)/2

Let, DB = d1 = 8 cm and CA = d2.

Area of a rhombus = (d1 × d2)/2

⇒ (d1 × d2)/2 = 24

⇒ 8 × d2 = 48

⇒ d2 = 48/8

⇒ d2 = 6

Hence, AC = 6 cm.

Thus, the area of the rhombus with side 5 cm and altitude 4.8 cm is 24 cm2, and the length of the other diagonal is 6 cm.

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