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.
Rhombus is a parallelogram with all sides equal to each other.
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.
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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