Question

6. 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.
its area.
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Answer 1

Answer:

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

rhombus ABCD

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