Find area of rhombus in which side is 5 cm and altitude is 4.8 cm. If one diagonal is 8 cm find length of other diagonal.
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.
Let's draw the diagram of rhombus ABCD, then find the area and the length of the other diagonal.
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
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.